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A CONTINUUM OF C*-NORMS ON ${\mathbb B}$(H) ⊗ ${\mathbb B}$(H) AND RELATED TENSOR PRODUCTS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  22 July 2015

NARUTAKA OZAWA  and
GILLES PISIER
NARUTAKA OZAWA
Affiliation:
RIMS, Kyoto University, 606-8502, Japan e-mail: narutaka@kurims.kyoto-u.ac.jp
GILLES PISIER
Affiliation:
Texas A&M University, College Station, TX 77843, USA and Université Paris VI, IMJ, Equipe d'Analyse Fonctionnelle, Paris 75252, France e-mail: pisier@math.tamu.edu
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Abstract

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For any pair M, N of von Neumann algebras such that the algebraic tensor product M ⊗ N admits more than one C*-norm, the cardinal of the set of C*-norms is at least 2ℵ0. Moreover, there is a family with cardinality 2ℵ0 of injective tensor product functors for C*-algebras in Kirchberg's sense. Let ${\mathbb B}$=∏nMn. We also show that, for any non-nuclear von Neumann algebra M⊂ ${\mathbb B}$(ℓ2), the set of C*-norms on ${\mathbb B}$ ⊗ M has cardinality equal to 22ℵ0.

MSC classification

Primary: 46L06: Tensor products of $C^*$-algebras 46L07: Operator spaces and completely bounded maps
Secondary: 46L09: Free products of $C^*$-algebras 46L10: General theory of von Neumann algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 2 , May 2016 , pp. 433 - 443
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

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