# A Remark on W*-Tensor Products of W*-Algebras

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## Abstract

Let is continuous. We define for every is a bijective isometry of ordered involutive Banach spaces (where this structure on

*E*be a W*-algebra,*T*a hyperstonian compact space,*C*(*T*) the W*-algebra of continuous scalar valued functions on*T*, and*F*(*T,E*) the set of bounded maps*x*:*T*→*E*such that for every element*a*of the predual of*E*the function$$T \to {\rm{IK,}}\,\,\,\,\,\,\,\,\,t \mapsto \langle x_t ,a\rangle $$

*x*∈*F*(*T,E*) an element \(\tilde x\) ∈*C*(*T*)\(\bar \otimes \)*E*such that the map$$f(T,E) \to b(T)\bar \otimes E,\,\,\,\,\,\,\,x \mapsto \tilde x$$

*F*(*T,E*) is defined pointwise). In general*F*(*T,E*) is not an algebra for the pointwise multiplication, but for*x,y,z*∈*F*(*T,E*) we characterize the case when \(\tilde x\tilde y = \tilde z\).## Keywords

Hilbert Space Tensor Product Orthogonal Projection Pairwise Disjoint Dual Norm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- 1.Constantinescu, C.,
*C*-algebras*, Elsevir, 2001.Google Scholar - 2.Takesaki, M.,
*Theory of Operator Algebra I,*Springer, 2002.Google Scholar - 3.Wegge-Olsen, N. E.,
*K-theory and C*-algebras,*Oxford University Press, 1993.Google Scholar

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