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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Categorical $ W\sp{\ast} $-tensor product


Author: John Dauns
Journal: Trans. Amer. Math. Soc. 166 (1972), 439-456
MSC: Primary 46L10; Secondary 46M05
DOI: https://doi.org/10.1090/S0002-9947-1972-0295093-6
MathSciNet review: 0295093
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Abstract: If A and B are von Neumann algebras and $ A\bar \otimes B$ denotes their categorical $ {C^ \ast }$-tensor product with the universal property, then the von Neumann tensor product $ A\nabla B$ of A and B is defined as

$\displaystyle A\nabla B = {(A\bar \otimes B)^{ \ast \ast }}/J,$

where $ J \subset {(A\bar \otimes B)^{\ast \ast}}$ is an appropriate ideal. It has the universal property.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0295093-6
Keywords: von Neumann algebra, predual, categorical $ {C^ \ast }$-tensor product, normal, singular functionals, functors of multiplicative categories, adjoint functor, cogebras, bigebras
Article copyright: © Copyright 1972 American Mathematical Society