Universal $$C^*$$-algebras of some properties
Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $...
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| Autor*in: |
Liu, Yifan [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Anmerkung: |
© Tusi Mathematical Research Group (TMRG) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Banach journal of mathematical analysis - Springer International Publishing, 2007, 18(2024), 4 vom: 18. Juli |
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| Übergeordnetes Werk: |
volume:18 ; year:2024 ; number:4 ; day:18 ; month:07 |
| Links: |
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| DOI / URN: |
10.1007/s43037-024-00372-8 |
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| Katalog-ID: |
SPR056646585 |
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| 520 | |a Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example. | ||
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| 650 | 4 | |a -algebras |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stable rank |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Small projection property |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stable exponential length |7 (dpeaa)DE-He213 | |
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10.1007/s43037-024-00372-8 doi (DE-627)SPR056646585 (SPR)s43037-024-00372-8-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Liu, Yifan verfasserin (orcid)0000-0003-2999-8428 aut Universal $$C^*$$-algebras of some properties 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Tusi Mathematical Research Group (TMRG) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example. Universal (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Stable rank (dpeaa)DE-He213 Small projection property (dpeaa)DE-He213 Stable exponential length (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 4 vom: 18. Juli (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:4 day:18 month:07 https://dx.doi.org/10.1007/s43037-024-00372-8 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-MATHE SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 AR 18 2024 4 18 07 |
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10.1007/s43037-024-00372-8 doi (DE-627)SPR056646585 (SPR)s43037-024-00372-8-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Liu, Yifan verfasserin (orcid)0000-0003-2999-8428 aut Universal $$C^*$$-algebras of some properties 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Tusi Mathematical Research Group (TMRG) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example. Universal (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Stable rank (dpeaa)DE-He213 Small projection property (dpeaa)DE-He213 Stable exponential length (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 4 vom: 18. Juli (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:4 day:18 month:07 https://dx.doi.org/10.1007/s43037-024-00372-8 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-MATHE SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 AR 18 2024 4 18 07 |
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10.1007/s43037-024-00372-8 doi (DE-627)SPR056646585 (SPR)s43037-024-00372-8-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Liu, Yifan verfasserin (orcid)0000-0003-2999-8428 aut Universal $$C^*$$-algebras of some properties 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Tusi Mathematical Research Group (TMRG) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example. Universal (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Stable rank (dpeaa)DE-He213 Small projection property (dpeaa)DE-He213 Stable exponential length (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 4 vom: 18. Juli (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:4 day:18 month:07 https://dx.doi.org/10.1007/s43037-024-00372-8 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-MATHE SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 AR 18 2024 4 18 07 |
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10.1007/s43037-024-00372-8 doi (DE-627)SPR056646585 (SPR)s43037-024-00372-8-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Liu, Yifan verfasserin (orcid)0000-0003-2999-8428 aut Universal $$C^*$$-algebras of some properties 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Tusi Mathematical Research Group (TMRG) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example. Universal (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Stable rank (dpeaa)DE-He213 Small projection property (dpeaa)DE-He213 Stable exponential length (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 4 vom: 18. Juli (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:4 day:18 month:07 https://dx.doi.org/10.1007/s43037-024-00372-8 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-MATHE SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 AR 18 2024 4 18 07 |
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10.1007/s43037-024-00372-8 doi (DE-627)SPR056646585 (SPR)s43037-024-00372-8-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Liu, Yifan verfasserin (orcid)0000-0003-2999-8428 aut Universal $$C^*$$-algebras of some properties 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Tusi Mathematical Research Group (TMRG) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example. Universal (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Stable rank (dpeaa)DE-He213 Small projection property (dpeaa)DE-He213 Stable exponential length (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 4 vom: 18. Juli (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:4 day:18 month:07 https://dx.doi.org/10.1007/s43037-024-00372-8 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER FID-MATHE SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_72 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2574 GBV_ILN_4029 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4116 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4155 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4598 GBV_ILN_4700 AR 18 2024 4 18 07 |
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English |
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Enthalten in Banach journal of mathematical analysis 18(2024), 4 vom: 18. Juli volume:18 year:2024 number:4 day:18 month:07 |
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Enthalten in Banach journal of mathematical analysis 18(2024), 4 vom: 18. Juli volume:18 year:2024 number:4 day:18 month:07 |
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Universal -algebras Stable rank Small projection property Stable exponential length |
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Universal</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-algebras</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stable rank</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Small projection property</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stable exponential length</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Banach journal of mathematical analysis</subfield><subfield code="d">Springer International Publishing, 2007</subfield><subfield code="g">18(2024), 4 vom: 18. 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Liu, Yifan |
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Liu, Yifan ddc 510 fid MATHE misc Universal misc -algebras misc Stable rank misc Small projection property misc Stable exponential length Universal $$C^*$$-algebras of some properties |
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510 VZ MATHE DE-7 fid Universal $$C^*$$-algebras of some properties Universal (dpeaa)DE-He213 -algebras (dpeaa)DE-He213 Stable rank (dpeaa)DE-He213 Small projection property (dpeaa)DE-He213 Stable exponential length (dpeaa)DE-He213 |
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ddc 510 fid MATHE misc Universal misc -algebras misc Stable rank misc Small projection property misc Stable exponential length |
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ddc 510 fid MATHE misc Universal misc -algebras misc Stable rank misc Small projection property misc Stable exponential length |
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universal $$c^*$$-algebras of some properties |
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Universal $$C^*$$-algebras of some properties |
| abstract |
Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example. © Tusi Mathematical Research Group (TMRG) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example. © Tusi Mathematical Research Group (TMRG) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract Let (P) be a property of $$C^*$$-algebras which may be satiesfied or not, and $$\mathscr {S}(P)$$ be the set of separable $$C^*$$-algebras which satiesfies (P). We give a sufficient condition for (P) to admit a universal separable element $$A\in \mathscr {S}(P)$$ in the sense that for any $$B\in \mathscr {S}(P)$$, there exists a surjective $$*$$-homomorphism $$\pi :A\rightarrow B$$, and use the sufficient condition to show that when (P) is “unital with stable rank n”, “the small projection property” or “unital with stable exponential lenght b”, the sufficient condition is satisfied and hence there exists a corresponding universal $$C^*$$-algebra. We also give a stronger condition for property (P), which additionally implies that the set of corresponding universal $$C^*$$-algebras is uncountable, and use it to show that the set of universal unital separable $$C^*$$-algebras of stable rank n is uncountable as an example. © Tusi Mathematical Research Group (TMRG) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| container_issue |
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| title_short |
Universal $$C^*$$-algebras of some properties |
| url |
https://dx.doi.org/10.1007/s43037-024-00372-8 |
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| doi_str |
10.1007/s43037-024-00372-8 |
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2024-10-24T04:55:48.881Z |
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| score |
7.1696415 |