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Proceedings of the American Mathematical Society

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

 

 

Equivalence of projections


Author: S. K. Berberian
Journal: Proc. Amer. Math. Soc. 33 (1972), 485-490
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1972-0295090-6
MathSciNet review: 0295090
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Abstract: Theorem: An $ A{W^\ast}$-algebra is the ring generated by its projections if and only if it has no abelian summand. Corollary: Every equivalence in an $ A{W^\ast}$-algebra may be implemented by a partial isometry in the ring generated by the projections of the algebra. The corollary is extended to certain finite Baer $ \ast $-rings.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0295090-6
Keywords: von Neumann algebra, $ A{W^\ast}$-algebra, Baer $ \ast $-ring
Article copyright: © Copyright 1972 American Mathematical Society