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Abstract:

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.

Registro:

Documento: Artículo
Título:A geometric characterization of nuclearity and injectivity
Autor:Andruchow, E.; Corach, G.; Stojanoff, D.
Filiación:Instituto Argentino de Matemâtica, Viamonte 1636 ler piso, 1035 Buenos Aires, Argentina
Departamento de Matemâtica, Facultad de Ciencias Exactas, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Año:1995
Volumen:133
Número:2
Página de inicio:474
Página de fin:494
DOI: http://dx.doi.org/10.1006/jfan.1995.1134
Título revista:Journal of Functional Analysis
Título revista abreviado:J. Funct. Anal.
ISSN:00221236
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v133_n2_p474_Andruchow

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Citas:

---------- APA ----------
Andruchow, E., Corach, G. & Stojanoff, D. (1995) . A geometric characterization of nuclearity and injectivity. Journal of Functional Analysis, 133(2), 474-494.
http://dx.doi.org/10.1006/jfan.1995.1134
---------- CHICAGO ----------
Andruchow, E., Corach, G., Stojanoff, D. "A geometric characterization of nuclearity and injectivity" . Journal of Functional Analysis 133, no. 2 (1995) : 474-494.
http://dx.doi.org/10.1006/jfan.1995.1134
---------- MLA ----------
Andruchow, E., Corach, G., Stojanoff, D. "A geometric characterization of nuclearity and injectivity" . Journal of Functional Analysis, vol. 133, no. 2, 1995, pp. 474-494.
http://dx.doi.org/10.1006/jfan.1995.1134
---------- VANCOUVER ----------
Andruchow, E., Corach, G., Stojanoff, D. A geometric characterization of nuclearity and injectivity. J. Funct. Anal. 1995;133(2):474-494.
http://dx.doi.org/10.1006/jfan.1995.1134