Lipschitz-free spaces and approximating sequences of projections
Abstract The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property...
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| Autor*in: |
Godefroy, Gilles [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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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), 2 vom: 19. März |
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| Übergeordnetes Werk: |
volume:18 ; year:2024 ; number:2 ; day:19 ; month:03 |
| Links: |
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| DOI / URN: |
10.1007/s43037-024-00332-2 |
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| Katalog-ID: |
SPR055218695 |
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| 520 | |a Abstract The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. It follows in particular that the $$(\pi )$$-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided. | ||
| 650 | 4 | |a Lipschitz-free spaces |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Absolute extendability |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Finite-dimensional decompositions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bounded approximation properties |7 (dpeaa)DE-He213 | |
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| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s43037-024-00332-2 |m X:SPRINGER |x Resolving-System |z lizenzpflichtig |3 Volltext |
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10.1007/s43037-024-00332-2 doi (DE-627)SPR055218695 (SPR)s43037-024-00332-2-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Godefroy, Gilles verfasserin aut Lipschitz-free spaces and approximating sequences of projections 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 The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. It follows in particular that the $$(\pi )$$-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided. Lipschitz-free spaces (dpeaa)DE-He213 Absolute extendability (dpeaa)DE-He213 Finite-dimensional decompositions (dpeaa)DE-He213 Bounded approximation properties (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 2 vom: 19. März (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:2 day:19 month:03 https://dx.doi.org/10.1007/s43037-024-00332-2 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_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_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 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_4700 AR 18 2024 2 19 03 |
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10.1007/s43037-024-00332-2 doi (DE-627)SPR055218695 (SPR)s43037-024-00332-2-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Godefroy, Gilles verfasserin aut Lipschitz-free spaces and approximating sequences of projections 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 The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. It follows in particular that the $$(\pi )$$-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided. Lipschitz-free spaces (dpeaa)DE-He213 Absolute extendability (dpeaa)DE-He213 Finite-dimensional decompositions (dpeaa)DE-He213 Bounded approximation properties (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 2 vom: 19. März (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:2 day:19 month:03 https://dx.doi.org/10.1007/s43037-024-00332-2 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_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_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 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_4700 AR 18 2024 2 19 03 |
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10.1007/s43037-024-00332-2 doi (DE-627)SPR055218695 (SPR)s43037-024-00332-2-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Godefroy, Gilles verfasserin aut Lipschitz-free spaces and approximating sequences of projections 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 The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. It follows in particular that the $$(\pi )$$-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided. Lipschitz-free spaces (dpeaa)DE-He213 Absolute extendability (dpeaa)DE-He213 Finite-dimensional decompositions (dpeaa)DE-He213 Bounded approximation properties (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 2 vom: 19. März (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:2 day:19 month:03 https://dx.doi.org/10.1007/s43037-024-00332-2 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_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_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 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_4700 AR 18 2024 2 19 03 |
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10.1007/s43037-024-00332-2 doi (DE-627)SPR055218695 (SPR)s43037-024-00332-2-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Godefroy, Gilles verfasserin aut Lipschitz-free spaces and approximating sequences of projections 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 The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. It follows in particular that the $$(\pi )$$-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided. Lipschitz-free spaces (dpeaa)DE-He213 Absolute extendability (dpeaa)DE-He213 Finite-dimensional decompositions (dpeaa)DE-He213 Bounded approximation properties (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 2 vom: 19. März (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:2 day:19 month:03 https://dx.doi.org/10.1007/s43037-024-00332-2 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_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_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 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_4700 AR 18 2024 2 19 03 |
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10.1007/s43037-024-00332-2 doi (DE-627)SPR055218695 (SPR)s43037-024-00332-2-e DE-627 ger DE-627 rakwb eng 510 VZ MATHE DE-7 fid Godefroy, Gilles verfasserin aut Lipschitz-free spaces and approximating sequences of projections 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 The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. It follows in particular that the $$(\pi )$$-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided. Lipschitz-free spaces (dpeaa)DE-He213 Absolute extendability (dpeaa)DE-He213 Finite-dimensional decompositions (dpeaa)DE-He213 Bounded approximation properties (dpeaa)DE-He213 Enthalten in Banach journal of mathematical analysis Springer International Publishing, 2007 18(2024), 2 vom: 19. März (DE-627)549633782 (DE-600)2395499-1 1735-8787 nnns volume:18 year:2024 number:2 day:19 month:03 https://dx.doi.org/10.1007/s43037-024-00332-2 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_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_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 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_4700 AR 18 2024 2 19 03 |
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Godefroy, Gilles |
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Godefroy, Gilles ddc 510 fid MATHE misc Lipschitz-free spaces misc Absolute extendability misc Finite-dimensional decompositions misc Bounded approximation properties Lipschitz-free spaces and approximating sequences of projections |
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lipschitz-free spaces and approximating sequences of projections |
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Lipschitz-free spaces and approximating sequences of projections |
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Abstract The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. It follows in particular that the $$(\pi )$$-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided. © 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 The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. It follows in particular that the $$(\pi )$$-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided. © 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 The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. It follows in particular that the $$(\pi )$$-property up to a logarithmic factor fails to imply the approximation property. A list of commented open problems is provided. © 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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Lipschitz-free spaces and approximating sequences of projections |
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https://dx.doi.org/10.1007/s43037-024-00332-2 |
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10.1007/s43037-024-00332-2 |
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2024-07-03T14:08:38.637Z |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR055218695</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20240424064741.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">240320s2024 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s43037-024-00332-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR055218695</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s43037-024-00332-2-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MATHE</subfield><subfield code="q">DE-7</subfield><subfield code="2">fid</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Godefroy, Gilles</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lipschitz-free spaces and approximating sequences of projections</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2024</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© 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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The Lipschitz-free space $${\mathcal {F}}(M)$$ has an F.D.D. when M is a separable $${\mathcal {L}}_1$$-Banach space, or when $$M\subset {\mathbb {R}}^n$$ is a somewhat regular subset. The interplay between the existence of extension operators for Lipschitz maps and the $$(\pi )$$-property in Lipschitz-free spaces is investigated. If M is an arbitrary metric space, then $${\mathcal {F}}(M)$$ has the $$(\pi )$$-property up to a universal logarithmic factor. 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