Locally convex quasi C$^*$-algebras and noncommutative integration
Volume 228 / 2015
Studia Mathematica 228 (2015), 33-45
MSC: Primary 46L08; Secondary 46L51, 47L60.
DOI: 10.4064/sm228-1-4
Abstract
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 topology and we focus our attention on the so-called locally convex quasi $C^*$-algebras. We show, in particular, that any strongly *-semisimple locally convex quasi C$^*$-algebra $({\mathfrak X},{\mathfrak A}_{0})$ can be represented in a class of noncommutative local $L^2$-spaces.
