Perturbations of C*-Algebraic Invariants Academic Article uri icon

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. © 2010 Springer Basel AG.

author list (cited authors)

  • Christensen, E., Sinclair, A., Smith, R. R., & White, S.

citation count

  • 14

complete list of authors

  • Christensen, Erik||Sinclair, Allan||Smith, Roger R||White, Stuart

publication date

  • June 2010