Structure of locally convex quasi $C^*$-algebras

TL;DR

This paper investigates the structure of locally convex quasi $C^*$-algebras, which generalize $C^*$-algebras by considering completions under certain topologies that lead to quasi *-algebras, with examples and structural analysis.

Contribution

It introduces and analyzes the structure of locally convex quasi $C^*$-algebras, extending the theory of $C^*$-algebras within the framework of quasi *-algebras.

Findings

Examples of locally convex quasi $C^*$-algebras are provided.

The structural properties of these quasi $C^*$-algebras are investigated.

Abstract

The completion of a (normed) $C^*$-algebra $A_0[\| \cdot \|_0]$ with respect to a locally convex topology $\tau$ 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.