A geometric characterization of nuclearity and injectivity
Let R(A, N) be the space of bounded non-degenerate representations π: A → N, where A is a nuclear C*-algebra and N an injective von Neumann algebra with separable predual. We prove that R(A, N) is an homogeneous reductive space under the action of the group GN, of invertible elements of N, and also...
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todo:paper_00221236_v133_n2_p474_Andruchow2023-10-03T14:27:13Z A geometric characterization of nuclearity and injectivity Andruchow, E. Corach, G. Stojanoff, D. Let R(A, N) be the space of bounded non-degenerate representations π: A → N, where A is a nuclear C*-algebra and N an injective von Neumann algebra with separable predual. We prove that R(A, N) is an homogeneous reductive space under the action of the group GN, of invertible elements of N, and also an analytic submanifold of L(A, N). The same is proved for the space of unital ultraweakly continuous bounded representations from an injective von Neumann algebra M into N. We prove also that the existence of a reductive structure for R(A, L(H)) is sufficient for A to be nuclear (and injective in the von Neumann case). Most of the known examples of Banach homogeneous reductive spaces (see [AS2], [ARS], [CPR2], [MR] and [M]) are particular cases of this construction, which moreover generalizes them, for example, to representations of amenable, type I or almost connected groups. © 1995 Academic Press Limited. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221236_v133_n2_p474_Andruchow |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
Let R(A, N) be the space of bounded non-degenerate representations π: A → N, where A is a nuclear C*-algebra and N an injective von Neumann algebra with separable predual. We prove that R(A, N) is an homogeneous reductive space under the action of the group GN, of invertible elements of N, and also an analytic submanifold of L(A, N). The same is proved for the space of unital ultraweakly continuous bounded representations from an injective von Neumann algebra M into N. We prove also that the existence of a reductive structure for R(A, L(H)) is sufficient for A to be nuclear (and injective in the von Neumann case). Most of the known examples of Banach homogeneous reductive spaces (see [AS2], [ARS], [CPR2], [MR] and [M]) are particular cases of this construction, which moreover generalizes them, for example, to representations of amenable, type I or almost connected groups. © 1995 Academic Press Limited. |
| format |
JOUR |
| author |
Andruchow, E. Corach, G. Stojanoff, D. |
| spellingShingle |
Andruchow, E. Corach, G. Stojanoff, D. A geometric characterization of nuclearity and injectivity |
| author_facet |
Andruchow, E. Corach, G. Stojanoff, D. |
| author_sort |
Andruchow, E. |
| title |
A geometric characterization of nuclearity and injectivity |
| title_short |
A geometric characterization of nuclearity and injectivity |
| title_full |
A geometric characterization of nuclearity and injectivity |
| title_fullStr |
A geometric characterization of nuclearity and injectivity |
| title_full_unstemmed |
A geometric characterization of nuclearity and injectivity |
| title_sort |
geometric characterization of nuclearity and injectivity |
| url |
http://hdl.handle.net/20.500.12110/paper_00221236_v133_n2_p474_Andruchow |
| work_keys_str_mv |
AT andruchowe ageometriccharacterizationofnuclearityandinjectivity AT corachg ageometriccharacterizationofnuclearityandinjectivity AT stojanoffd ageometriccharacterizationofnuclearityandinjectivity AT andruchowe geometriccharacterizationofnuclearityandinjectivity AT corachg geometriccharacterizationofnuclearityandinjectivity AT stojanoffd geometriccharacterizationofnuclearityandinjectivity |
| _version_ |
1807322750352621568 |