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On tensor products of operator modules. (English) Zbl 1119.46313

Summary: The injective tensor product of normal representable bimodules over von Neumann algebras is shown to be normal. The usual Banach module projective tensor product of central representable bimodules over an Abelian \(C^*\)-algebra is shown to be representable. A normal version of the projective tensor product is introduced for central normal bimodules.

MSC:

46L07 Operator spaces and completely bounded maps
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
47L25 Operator spaces (= matricially normed spaces)
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