Perturbations of C*-Algebraic Invariants
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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. © 2010 Springer Basel AG.
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Christensen, E., Sinclair, A., Smith, R. R., & White, S.
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Christensen, Erik||Sinclair, Allan||Smith, Roger R||White, Stuart
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Close Operator Algebras
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Finite Length
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Perturbations
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Similarity Problem
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