Topological partial * - algebras : Basic properties and examples

Let A be a partial *-algebra endowed with a topology that makes it into a locally convex topological vector space AA]. Then A is called a topological partial *-algebra if it satisses a number of conditions, which all amount to require that the topology ts with the multiplier structure of A. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of potential topological partial *-algebras, either function spaces (lattices of L p spaces on 0; 1] or on R, amalgam spaces), or partial *-algebras of operators (operators on a partial inner product space, O*-algebras).