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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46K05, 16W10, 46L10

Retrieve articles in all journals with MSC: 46K05, 16W10, 46L10

Additional Information

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