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 Fillmoreâs 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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