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Transactions of the American Mathematical Society

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



On the tensor product of $ W\sp{\ast} $ algebras

Author: Bruce B. Renshaw
Journal: Trans. Amer. Math. Soc. 194 (1974), 337-347
MSC: Primary 46L10
MathSciNet review: 0361815
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Abstract: We develop the algebra underlying the reduction theory of von Neumann in the language and spirit of Sakai's abstract $ {W^ \ast }$ algebras, and using the maximum spectrum of an abelian von Neumann algebra rather than a measure-theoretic surrogate. We are thus enabled to obtain the basic fact of the von Neumann theory as a special case of a weaker general decomposition theorem, valid without separability or type restrictions, and adapted to comparison with Wright's theory in the finite case.

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Keywords: Reduction theory, $ {W^\ast}$ algebra, normed modules, $ {W^ \ast }$ topology, von Neumann algebra, hyperstonean space, primary decomposition
Article copyright: © Copyright 1974 American Mathematical Society