Moduli di Banach su -algebre: rappresentazioni Hilbertiane ed in spazi non commutativi
Representations of modules over a *-algebra and related seminorms
Representations of a module over a *-algebra are considered and some related seminorms are constructed and studied, with the aim of finding bounded *-representations of .
Locally convex quasi C*-algebras and noncommutative integration
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.
Quasi *-algebras of measurable operators
Non-commutative -spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. CQ*-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (,₀) with a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra...
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