PERTURBATIONS OF C*-ALGEBRAIC INVARIANTS Academic Article

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.

authors

• Smith, Roger

published proceedings

• GEOMETRIC AND FUNCTIONAL ANALYSIS

author list (cited authors)

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

citation count

• 15

complete list of authors

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

publication date

• August 2010

publisher

• Springer Nature  Publisher

published in

• GEOMETRIC AND FUNCTIONAL ANALYSIS  Journal

keywords

• Close Operator Algebras
• Finite Length
• Perturbations
• Similarity Problem

Digital Object Identifier (DOI)

• 10.1007/s00039-010-0070-y

start page

• 368

end page

• 397

volume

• 20

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs00039-010-0070-y