Perturbations of C*-algebraic invariants

Abstract

Kadison and Kastler introduced a metric on the set of all C${}^{\ast }$-algebras on a fixed Hilbert space. In this paper structural properties of C${}^{\ast }$-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${}^{\ast }$-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${}^{\ast }$-algebras, showing that sufficiently close algebras have isomorphic Elliott invariants when one algebra has the similarity property.

29 Pages

Cited by in corpus (5)

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