2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225959The completion of a (normed) $C^*$-algebra $A_0[\| \cdot \|_0]$ with respect to a locally convex topology $τ$ on $A_0$ that makes the multiplication of $A_0$ separately continuous is, in general, a quasi *-algebra, and not a locally convex *-algebra. 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.Mathematical Physicstext