Perturbations of C*-algebraic Invariants

Erik Christensen; Allan M. Sinclair; Roger R. Smith; Stuart White

Perturbations of C*-algebraic Invariants

Erik Christensen, Allan M. Sinclair, Roger R. Smith, Stuart White

Department of Mathematical Sciences

14 Citations (Scopus)

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.

Original language	English
Journal	Geometric and Functional Analysis
Volume	20
Issue number	2
Pages (from-to)	368 - 397
Number of pages	30
ISSN	1016-443X
Publication status	Published - 2010

Cite this

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title = "Perturbations of C*-algebraic Invariants",

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.",

author = "Erik Christensen and Sinclair, {Allan M.} and Smith, {Roger R.} and Stuart White",

year = "2010",

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journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Springer Basel AG",

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T1 - Perturbations of C*-algebraic Invariants

AU - Christensen, Erik

AU - Sinclair, Allan M.

AU - Smith, Roger R.

AU - White, Stuart

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

M3 - Journal article

SN - 1016-443X

VL - 20

SP - 368

EP - 397

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 2

ER -

Perturbations of C*-algebraic Invariants

Abstract

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