Locally convex quasi C*-algebras and noncommutative integration

TL;DR

This paper investigates the structure of locally convex quasi C*-algebras, demonstrating their representation within noncommutative local L^2-spaces, thereby extending the understanding of noncommutative integration.

Contribution

It establishes that strongly *-semisimple locally convex quasi C*-algebras can be represented in noncommutative local L^2-spaces, advancing the theory of noncommutative integration.

Findings

Representation of quasi C*-algebras in noncommutative L^2-spaces

Extension of noncommutative integration framework

Analysis of structures as completions of C*-algebras

Abstract

In this paper we continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm and we focus our attention on the so-called {\em locally convex quasi C*-algebras}. We show, in particular, that any strongly *-semisimple locally convex quasi C*-algebra $(\X,\Ao)$, can be represented in a class of noncommutative local $L^2$-spaces.