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A CONTINUUM OF C*-NORMS ON
${\mathbb B}$(H) ⊗
${\mathbb B}$(H) AND RELATED TENSOR PRODUCTS
Published online by Cambridge University Press: 22 July 2015
Abstract
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.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 2015
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