Extension of representations in quasi *-algebras

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Abstract

Let $(\A, \A_o)$ be a topological \qxa, which means in particular that $\A_o$is a topological \xa, dense in \A. Let $\pi^o$ be a *-representation of $\A_o$in some pre-Hilbert space $\D \subset \H$. Then we present several ways of extending $\pi^o$, by closure, to some larger \qxa\ contained in \A, either by Hilbert space operators,or by sesquilinear forms on \D.Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.
Original languageEnglish
Pages (from-to)241-264
Number of pages24
JournalANNALES DE L'INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE
Volume69
Publication statusPublished - 1998

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