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 | References | Similar Articles | Additional Information
Abstract: We develop the algebra underlying the reduction theory of von Neumann in the language and spirit of Sakaiâs 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 Wrightâs theory in the finite case.
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Additional Information
Keywords:
Reduction theory,
<IMG WIDTH="37" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${W^\ast }$"> algebra,
normed modules,
<!â MATH ${W^ \ast }$ â> <IMG WIDTH="37" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img7.gif" ALT="${W^ \ast }$"> topology,
von Neumann algebra,
hyperstonean space,
primary decomposition
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© Copyright 1974
American Mathematical Society