Structure of locally convex quasi C^*-algebras

Abstract

The completion of a (normed) C^*-algebra $\mathscr{A}$₀[|| · ||₀] with respect to a locally convex topology τ on $\mathscr{A}$₀ that makes the multiplication of $\mathscr{A}$₀ separately continuous is, in general, a quasi *-algebra, and not a locally convex *-algebra [10], [15]. In this way, one is led to consideration of locally convex quasi C^*-algebras, which generalize C^*-algebras in the context of quasi *-algebras. Examples are given and the structure of these relatives of C^*-algebras is investigated.