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Transactions of the American Mathematical Society

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

 
 

 

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


Author: Bruce B. Renshaw
Journal: Trans. Amer. Math. Soc. 194 (1974), 337-347
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9947-1974-0361815-0
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, <IMG WIDTH="37" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${W^\ast }$"> algebra, normed modules, <!– MATH ${W^ \ast }$ –> <IMG WIDTH="37" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img7.gif" ALT="${W^ \ast }$"> topology, von Neumann algebra, hyperstonean space, primary decomposition
Article copyright: © Copyright 1974 American Mathematical Society