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 -rings and prove that Fillmore's result is true if *A* is a properly infinite Baer -ring satisfying (ENCP) and . This also affirmatively answers the open problem on -algebras posed by Berberian.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1995-1224621-X

Keywords:
Baer -rings,
-algebras,
unitary,
symmetry in -rings,
existence of noncentral projection axiom,
generalized comparability,

Article copyright:
© Copyright 1995
American Mathematical Society