Journal of Operator Theory

Volume 54, Issue 2, Fall 2005 pp. 317-337.

On tensor products of operator modules

Authors: Bojan Magajna
Author institution: Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia

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.

Keywords: Operator bimodule, von Neumann algebra, tensor norms

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