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HILBERT C*-BIMODULES OF FINITE INDEX AND APPROXIMATION PROPERTIES OF C*-ALGEBRAS

Part of: Selfadjoint operator algebras Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  17 October 2017

MARZIEH FOROUGH  and
MASSOUD AMINI
MARZIEH FOROUGH
Affiliation:
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran e-mails: [email protected], [email protected]
MASSOUD AMINI
Affiliation:
Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran School of Mathematics, Institute for Research in Fundamental Sciences, Tehran 19395-5746, Iran e-mails: [email protected], [email protected]
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Abstract

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Let A and B be arbitrary C*-algebras, we prove that the existence of a Hilbert A–B-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP are shared by A and B. For this, we first study the stability of the WEP, QWEP, and LLP under Morita equivalence of C*-algebras. We present examples of Hilbert A–B-bimodules, which are not of finite index, while such properties are shared between A and B. To this end, we study twisted crossed products by amenable discrete groups.

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46B28: Spaces of operators; tensor products; approximation properties 46L55: Noncommutative dynamical systems
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 2 , May 2018 , pp. 321 - 331
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

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