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.
Keywords:
continue analysis undertaken series previous papers structures arising completions * algebras under topologies coarser their norm topology focus attention so called locally convex quasi * algebras particular strongly * semisimple locally convex quasi * algebra mathfrak mathfrak represented class noncommutative local spaces
Affiliations des auteurs :
Camillo Trapani
1
;
Salvatore Triolo
2
1
Dipartimento di Matematica e Informatica Università di Palermo I-90123 Palermo, Italy
2
Dipartimento DEIM Università di Palermo I-90123 Palermo, Italy
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author = {Camillo Trapani and Salvatore Triolo},
title = {Locally convex quasi {C}$^*$-algebras and
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journal = {Studia Mathematica},
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language = {en},
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Camillo Trapani; Salvatore Triolo. Locally convex quasi C$^*$-algebras and
noncommutative integration. Studia Mathematica, Tome 228 (2015) no. 1, pp. 33-45. doi: 10.4064/sm228-1-4
