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Unitary equivalence of unbounded *-representations of *-algebras

Published online by Cambridge University Press:  01 September 1997

I. IKEDA ,
A. INOUE  and
M. TAKAKURA
I. IKEDA
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka, Japan
A. INOUE
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka, Japan
M. TAKAKURA
Affiliation:
Department of Applied Mathematics, Fukuoka University, Fukuoka, Japan
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Abstract

In this paper the unitary equivalence of unbounded *-representations of *-algebras is investigated. It is shown that if closed *-representations π1 and π2 of a *-algebra [Ascr] satisfy a certain density condition for the intertwining spaces [Jscr](π1, π2) and [Jscr](π2, π1), then a *-isomorphism Φ between the O*-algebras π1([Ascr]) and π2([Ascr]) is defined by Φ(π1(x))=π2(x), x∈[Ascr] and it induces a *-isomorphism Φ¯, between the von Neumann algebras (π1([Ascr])′w)′ and (π2([Ascr])′w)′, and further if Φ¯, is spatial (that is, it is unitarily implemented), then π1 and π2 are unitarily equivalent.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 2 , September 1997 , pp. 269 - 279
Copyright
Cambridge Philosophical Society 1997

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