Perturbations of C*-algebraic invariants

Christensen, E., Sinclair, A., Smith, R.R. and White, S. (2010) Perturbations of C*-algebraic invariants. Geometric and Functional Analysis, 20(2), pp. 368-397. (doi:10.1007/s00039-010-0070-y)

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Abstract

Kadison and Kastler introduced a metric on the set of all C*-algebras on a fixed Hilbert space. In this paper structural properties of C*-algebras which are close in this metric are examined. Our main result is that the property of having a positive answer to Kadison’s similarity problem transfers to close C*-algebras. In establishing this result we answer questions about closeness of commutants and tensor products when one algebra satisfies the similarity property. We also examine K-theory and traces of close C*-algebras, showing that sufficiently close algebras have isomorphic Elliott invariants when one algebra has the similarity property.

Item Type:Articles
Additional Information:The original publication is available at www.springerlink.com
Keywords:Close operator algebras, perturbations, similarity problem, finite length
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:White, Professor Stuart
Authors: Christensen, E., Sinclair, A., Smith, R.R., and White, S.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Geometric and Functional Analysis
Publisher:Springer (Birkhäuser Basel)
ISSN:1016-443X
ISSN (Online):1420-8970
Published Online:17 June 2010
Copyright Holders:Copyright © 2010 Springer
First Published:First published in Geometric And Functional Analysis 20(2):368-397
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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