EXTENSION OF REPRESENTATIONS IN QUASI ASTERISK-ALGEBRAS

Let (U, U-o) be a topological quasi -algebra, which means in particul ar that U-o is a topological -algebra, dense in U. Let pi(o) be a *-r epresentation of U-o in some pre-Hilbert space D subset of H. Then we present several ways of extending pi(o), by closure, to some larger qu asi -algebra contained in U, either by Hilbert space operators, or by sesquilinear forms on D. Explicit examples are discussed, both abelia n and nonabelian, including the CCR algebra. (C) Elsevier, Paris.