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

Institut for Matematiske Fag

14 Citationer (Scopus)

Abstract

Rammen for arbejdet er den såkaldte perturbationsteori for operatoralgebraer. Det vises at flere forskellige invarianter for C*-algebraer er stabile under perturbationer. Hovedresultatet viser, at det af Pisier indførte begrb, kaldet endelig længde fastholdes under passende små perturbationer.
Udgivelsesdato: August 2010

Originalsprog	Engelsk
Tidsskrift	Geometric and Functional Analysis
Vol/bind	20
Udgave nummer	2
Sider (fra-til)	368 - 397
Antal sider	30
ISSN	1016-443X
Status	Udgivet - 2010

Citationsformater

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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",

language = "English",

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journal = "Geometric and Functional Analysis",

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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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Citationsformater