Completely bounded mappings and simplicial complex structure in the primitive ideal space of a C*-algebra

Robert J Archbold, Douglas W B Somerset, Richard M. Timoney

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We consider the natural contraction from the central Haagerup tensor product of a C*-algebra A with itself to the space of completely bounded maps CB( A) on A and investigate those A where there exists an inverse map with finite norm L( A). We show that a stabilised version L'(A) = sup(n) L(M-n(A)) depends only on the primitive ideal space Prim(A). The dependence is via simplicial complex structures (defined from primal intersections) on finite sets of primitive ideals that contain a Glimm ideal of A. Moreover L'(A) = L(A circle times kappa( H)), with kappa(H) the compact operators, which requires us to develop the theory in the context of C*-algebras that are not necessarily unital.

Original languageEnglish
Pages (from-to)1397-1427
Number of pages31
JournalTransactions of the American Mathematical Society
Volume361
Issue number3
Early online date24 Oct 2008
DOIs
Publication statusPublished - Mar 2009

Keywords

  • Haagerup tensor product
  • operator-algebras
  • factorial states
  • primal ideals
  • lie-groups

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