On non-separable %$L^1%$-spaces of a vector measure
Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\ti...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Rodríguez, José [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales - Heidelberg [u.a.] : Springer, 2001, 111(2016), 4 vom: 25. Okt., Seite 1039-1050 |
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| Übergeordnetes Werk: |
volume:111 ; year:2016 ; number:4 ; day:25 ; month:10 ; pages:1039-1050 |
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| DOI / URN: |
10.1007/s13398-016-0345-8 |
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| Katalog-ID: |
SPR031581285 |
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| 100 | 1 | |a Rodríguez, José |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On non-separable %$L^1%$-spaces of a vector measure |
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| 520 | |a Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. Some other results on non-separable %$L^1%$ spaces of vector measures are given. | ||
| 650 | 4 | |a Vector measure |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Non-separable Banach space |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Space of integrable functions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Maharam type |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Space of bounded functions with countable support |7 (dpeaa)DE-He213 | |
| 773 | 0 | 8 | |i Enthalten in |t Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales |d Heidelberg [u.a.] : Springer, 2001 |g 111(2016), 4 vom: 25. Okt., Seite 1039-1050 |w (DE-627)495744433 |w (DE-600)2198482-7 |x 1579-1505 |7 nnns |
| 773 | 1 | 8 | |g volume:111 |g year:2016 |g number:4 |g day:25 |g month:10 |g pages:1039-1050 |
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10.1007/s13398-016-0345-8 doi (DE-627)SPR031581285 (SPR)s13398-016-0345-8-e DE-627 ger DE-627 rakwb eng 510 ASE Rodríguez, José verfasserin aut On non-separable %$L^1%$-spaces of a vector measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. Some other results on non-separable %$L^1%$ spaces of vector measures are given. Vector measure (dpeaa)DE-He213 Non-separable Banach space (dpeaa)DE-He213 Space of integrable functions (dpeaa)DE-He213 Maharam type (dpeaa)DE-He213 Space of bounded functions with countable support (dpeaa)DE-He213 Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 111(2016), 4 vom: 25. Okt., Seite 1039-1050 (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:111 year:2016 number:4 day:25 month:10 pages:1039-1050 https://dx.doi.org/10.1007/s13398-016-0345-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 111 2016 4 25 10 1039-1050 |
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10.1007/s13398-016-0345-8 doi (DE-627)SPR031581285 (SPR)s13398-016-0345-8-e DE-627 ger DE-627 rakwb eng 510 ASE Rodríguez, José verfasserin aut On non-separable %$L^1%$-spaces of a vector measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. Some other results on non-separable %$L^1%$ spaces of vector measures are given. Vector measure (dpeaa)DE-He213 Non-separable Banach space (dpeaa)DE-He213 Space of integrable functions (dpeaa)DE-He213 Maharam type (dpeaa)DE-He213 Space of bounded functions with countable support (dpeaa)DE-He213 Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 111(2016), 4 vom: 25. Okt., Seite 1039-1050 (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:111 year:2016 number:4 day:25 month:10 pages:1039-1050 https://dx.doi.org/10.1007/s13398-016-0345-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 111 2016 4 25 10 1039-1050 |
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10.1007/s13398-016-0345-8 doi (DE-627)SPR031581285 (SPR)s13398-016-0345-8-e DE-627 ger DE-627 rakwb eng 510 ASE Rodríguez, José verfasserin aut On non-separable %$L^1%$-spaces of a vector measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. Some other results on non-separable %$L^1%$ spaces of vector measures are given. Vector measure (dpeaa)DE-He213 Non-separable Banach space (dpeaa)DE-He213 Space of integrable functions (dpeaa)DE-He213 Maharam type (dpeaa)DE-He213 Space of bounded functions with countable support (dpeaa)DE-He213 Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 111(2016), 4 vom: 25. Okt., Seite 1039-1050 (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:111 year:2016 number:4 day:25 month:10 pages:1039-1050 https://dx.doi.org/10.1007/s13398-016-0345-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 111 2016 4 25 10 1039-1050 |
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10.1007/s13398-016-0345-8 doi (DE-627)SPR031581285 (SPR)s13398-016-0345-8-e DE-627 ger DE-627 rakwb eng 510 ASE Rodríguez, José verfasserin aut On non-separable %$L^1%$-spaces of a vector measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. Some other results on non-separable %$L^1%$ spaces of vector measures are given. Vector measure (dpeaa)DE-He213 Non-separable Banach space (dpeaa)DE-He213 Space of integrable functions (dpeaa)DE-He213 Maharam type (dpeaa)DE-He213 Space of bounded functions with countable support (dpeaa)DE-He213 Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 111(2016), 4 vom: 25. Okt., Seite 1039-1050 (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:111 year:2016 number:4 day:25 month:10 pages:1039-1050 https://dx.doi.org/10.1007/s13398-016-0345-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 111 2016 4 25 10 1039-1050 |
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10.1007/s13398-016-0345-8 doi (DE-627)SPR031581285 (SPR)s13398-016-0345-8-e DE-627 ger DE-627 rakwb eng 510 ASE Rodríguez, José verfasserin aut On non-separable %$L^1%$-spaces of a vector measure 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. Some other results on non-separable %$L^1%$ spaces of vector measures are given. Vector measure (dpeaa)DE-He213 Non-separable Banach space (dpeaa)DE-He213 Space of integrable functions (dpeaa)DE-He213 Maharam type (dpeaa)DE-He213 Space of bounded functions with countable support (dpeaa)DE-He213 Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 111(2016), 4 vom: 25. Okt., Seite 1039-1050 (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:111 year:2016 number:4 day:25 month:10 pages:1039-1050 https://dx.doi.org/10.1007/s13398-016-0345-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_2008 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 111 2016 4 25 10 1039-1050 |
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Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 111(2016), 4 vom: 25. Okt., Seite 1039-1050 volume:111 year:2016 number:4 day:25 month:10 pages:1039-1050 |
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Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales 111(2016), 4 vom: 25. Okt., Seite 1039-1050 volume:111 year:2016 number:4 day:25 month:10 pages:1039-1050 |
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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">SPR031581285</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220111192101.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2016 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s13398-016-0345-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR031581285</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s13398-016-0345-8-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">ASE</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rodríguez, José</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On non-separable %$L^1%$-spaces of a vector measure</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</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="520" ind1=" " ind2=" "><subfield code="a">Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. 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Rodríguez, José |
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Rodríguez, José ddc 510 misc Vector measure misc Non-separable Banach space misc Space of integrable functions misc Maharam type misc Space of bounded functions with countable support On non-separable %$L^1%$-spaces of a vector measure |
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510 ASE On non-separable %$L^1%$-spaces of a vector measure Vector measure (dpeaa)DE-He213 Non-separable Banach space (dpeaa)DE-He213 Space of integrable functions (dpeaa)DE-He213 Maharam type (dpeaa)DE-He213 Space of bounded functions with countable support (dpeaa)DE-He213 |
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ddc 510 misc Vector measure misc Non-separable Banach space misc Space of integrable functions misc Maharam type misc Space of bounded functions with countable support |
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ddc 510 misc Vector measure misc Non-separable Banach space misc Space of integrable functions misc Maharam type misc Space of bounded functions with countable support |
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On non-separable %$L^1%$-spaces of a vector measure |
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Rodríguez, José |
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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales |
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on non-separable %$l^1%$-spaces of a vector measure |
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On non-separable %$L^1%$-spaces of a vector measure |
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Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. Some other results on non-separable %$L^1%$ spaces of vector measures are given. |
| abstractGer |
Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. Some other results on non-separable %$L^1%$ spaces of vector measures are given. |
| abstract_unstemmed |
Abstract Let %$\kappa %$ be an infinite cardinal. Let %$\nu %$ be a (countably additive Banach space-valued) vector measure defined on a %$\sigma %$-algebra %$\Sigma %$. We prove that if %$\nu %$ is homogeneous and %$L^1(\nu )%$ has density character %$\kappa %$, then there is a vector measure %$\tilde{\nu }:\Sigma \rightarrow \ell ^\infty _{<}(\kappa )%$ such that %$L^1(\nu )=L^1(\tilde{\nu })%$ with equal norms. Here %$\ell ^\infty _{<}(\kappa )%$ denotes the subspace of %$\ell ^\infty (\kappa )%$ consisting of all %$(x_\alpha )_{\alpha <\kappa }\in \ell ^\infty (\kappa )%$ such that %$|\{\alpha<\kappa : |x_\alpha |>\varepsilon \}|<\kappa %$ for every %$\varepsilon >0%$. In this way, we extend to the non-separable setting a result of Curbera corresponding to the case %$\kappa =\omega %$. Some other results on non-separable %$L^1%$ spaces of vector measures are given. |
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4 |
| title_short |
On non-separable %$L^1%$-spaces of a vector measure |
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https://dx.doi.org/10.1007/s13398-016-0345-8 |
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| doi_str |
10.1007/s13398-016-0345-8 |
| up_date |
2024-07-04T00:23:13.810Z |
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| score |
7.397897 |