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PERTURBATIONS OF C*-ALGEBRAIC INVARIANTS

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Original languageEnglish
Pages (from-to)368-397
Number of pages30
JournalGeometric and Functional Analysis
Volume20
Issue number2
DOIs
Publication statusPublished - Aug 2010

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.

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