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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On $ W\sp{\ast} $ embedding of $ AW\sp{\ast} $-algebras


Author: Diane Laison
Journal: Proc. Amer. Math. Soc. 35 (1972), 499-502
MSC: Primary 46K99
DOI: https://doi.org/10.1090/S0002-9939-1972-0306928-8
MathSciNet review: 0306928
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Abstract: An $ A{W^ \ast }$-algebra N with a separating family of completely additive states and with a family $ \{ {e_\alpha }:\alpha \in A\} $ of mutually orthogonal projections such that $ {\operatorname{lub} _\alpha }{e_\alpha } = 1$ and $ {e_\alpha }N{e_\alpha }$ is a $ {W^ \ast }$-algebra for each $ \alpha \in A$ is shown to have a faithful representation as a ring of operators. This gives a new and considerably shorter proof that a semifinite $ A{W^ \ast }$-algebra with a separating family of completely additive states has a faithful representation as a ring of operators.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0306928-8
Article copyright: © Copyright 1972 American Mathematical Society