Extension of representations in quasi *-algebras

Details Extension of representations in quasi *-algebras Extension of representations in quasi *-algebras

2009-04-06

arxiv.org/abs/0904.0887v1

Ann. Inst. H. Poincar\'e, {\bf 69}, 241-264, (1998)

Physics

Mathematical Physics

Scientific paper

Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $\pi^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${\cal D} \subset {\cal H}$. Then we present several ways of extending $\pi^o$, by closure, to some larger quasi *-algebra contained in $A$, either by Hilbert space operators, or by sesquilinear forms on ${\cal D}$. Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.

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