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.
|Number of pages||24|
|Journal||ANNALES DE L'INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE|
|Publication status||Published - 1998|