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Tensor products which do not preserve operator algebras

Published online by Cambridge University Press:  24 October 2008

David P. Blecher
David P. Blecher
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204–3476, U.S.A.
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Extract

Of late the link between operator algebras and certain tensor products has been reiterated [5]. We prove here that the projective and Haagerup tensor products of two infinite-dimensional C*-algebras is not even topologically isomorphic to an algebra of operators on a Hilbert space. Estimates are given for the distance of the tensor product from such an algebra. Nonetheless with respect to a natural multiplication the Haagerup tensor product of two algebras of Hilbert space operators is completely isometrically isomorphic to an algebra of operators on some B(ℋ).

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Type
Research Article
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Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 395 - 403
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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