On the central Haagerup tensor product and completely bounded mappings of a C*-algebra

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

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13 Citations (Scopus)


We consider the natural contractive map from the central Haagerup, tensor product of a unital C*-algebra A with itself to the space of completely bounded maps CB(A) on A. We establish the necessity of the known sufficient condition for isometry of the map, namely that all Glimm ideals of A are primal. However, when the map is restricted to tensors with length bounded by a fixed quantity, a weaker necessary and sufficient condition is established. (c) 2005 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)406-428
Number of pages22
JournalJournal of Functional Analysis
Issue number2
Publication statusPublished - Sep 2005


  • Glimm ideal
  • primal ideal
  • matrix numerical range
  • MAPS

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