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Locally convex quasi C$^*$-algebras and noncommutative integration

Volume 228 / 2015

Camillo Trapani, Salvatore Triolo 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.

Authors

  • Camillo TrapaniDipartimento di Matematica e Informatica
    Università di Palermo
    I-90123 Palermo, Italy
    e-mail
  • Salvatore TrioloDipartimento DEIM
    Università di Palermo
    I-90123 Palermo, Italy
    e-mail

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