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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Publicado: 1995
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v133_n2_p474_Andruchow
http://hdl.handle.net/20.500.12110/paper_00221236_v133_n2_p474_Andruchow
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00221236_v133_n2_p474_Andruchow2023-06-08T14:46:22Z 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 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. 1995 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v133_n2_p474_Andruchow http://hdl.handle.net/20.500.12110/paper_00221236_v133_n2_p474_Andruchow
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection 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.
title A geometric characterization of nuclearity and injectivity
spellingShingle 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
publishDate 1995
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v133_n2_p474_Andruchow
http://hdl.handle.net/20.500.12110/paper_00221236_v133_n2_p474_Andruchow
_version_ 1768545404522070016

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