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 |
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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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