Perturbations of C*-algebraic invariants

Details Perturbations of C*-algebraic invariants Perturbations of C*-algebraic invariants

2009-10-07

arxiv.org/abs/0910.1368v1

Geom. Funct. Anal., 20 (2010) 368-397

Mathematics

Operator Algebras

29 Pages

Scientific paper

10.1007/s00039-010-0070-y

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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