On tensor products of operator modules

Abstract

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${}^{\ast }$-algebra is shown to be representable. A normal version of the projective tensor product is introduced for central normal bimodules.

16 pages, AMS LaTeX, to appear in J.O.T. This is the second, revised, part of the manuscript formerly entitled "Duality and normal parts..."