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ArticleOriginal scientific text

Title

Hilbert modules and tensor products of operator spaces

Authors 1

Affiliations

  1. Department of Mathematics, University of Ljubljana, Ljubljana 1000, Slovenia

Abstract

The classical identification of the predual of B(H) (the algebra of all bounded operators on a Hilbert space H) with the projective operator space tensor product H¯⨂^H is extended to the context of Hilbert modules over commutative von Neumann algebras. Each bounded module homomorphism b between Hilbert modules over a general C*-algebra is shown to be completely bounded with ∥b∥cb=∥b∥. The so called projective operator tensor product of two operator modules X and Y over an abelian von Neumann algebra C is introduced and if Y is a Hilbert module, this product is shown to coincide with the Haagerup tensor product of X and Y over C.

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Banach Center Publications
1997/38/1
Export to PBN, Opens in new tab
Pages:
227-246
Main language of publication
English
Published
1997
Exact and natural sciences