A CONTINUUM OF C*-NORMS ON ${\mathbb B}$(H) ⊗ ${\mathbb B}$(H) AND RELATED TENSOR PRODUCTS. (22nd July 2015)

• Record Type: Journal Article
• Authors: OZAWA, NARUTAKA; PISIER, GILLES
• Is Part Of: Glasgow mathematical journal. Volume 58:Part 2(2016)
• Page Start: 433
• Page End: 443
• Publication Date: 2015-07-22
• Subjects: Primary 46L06, -- 46L07, -- Secondary 46L09, -- 46L10; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0017089515000257
• Languages: English
• ISSNs: 0017-0895

Abstract

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 2 ℵ0 . Moreover, there is a family with cardinality 2 ℵ0 of injective tensor product functors for C*-algebras in Kirchberg's sense. Let ${\mathbb B}$ =∏ n M n . 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 2 2 ℵ0 .