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Locally convex quasi C*-algebras and noncommutative integration

Camillo Trapani, Salvatore Triolo (2015)

Studia Mathematica

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 (𝔛,𝔄₀) can be represented in a class of noncommutative local L²-spaces.

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