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Unitary equivalence of unbounded *-representations of *-algebras
Published online by Cambridge University Press: 01 September 1997
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