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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A unitary as a product of symmetries


Authors: N. K. Thakare and A. R. Baliga
Journal: Proc. Amer. Math. Soc. 123 (1995), 1005-1008
MSC: Primary 46K05; Secondary 16W10, 46L10
MathSciNet review: 1224621
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Abstract: It was proved by Fillmore that a unitary of a properly infinite von Neumann algebra A can be expressed as a product of at most four symmetries. In this paper we introduce an axiom (ENCP) for Baer $ ^ \ast $-rings and prove that Fillmore's result is true if A is a properly infinite Baer $ ^ \ast $-ring satisfying (ENCP) and $ LP \sim RP$. This also affirmatively answers the open problem on $ A{W^ \ast }$-algebras posed by Berberian.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1224621-X
PII: S 0002-9939(1995)1224621-X
Keywords: Baer $ ^ \ast $-rings, $ {\text{AW}^ \ast }$-algebras, unitary, symmetry in $ ^ \ast $-rings, existence of noncentral projection axiom, generalized comparability, $ LP \sim RP$
Article copyright: © Copyright 1995 American Mathematical Society