Search results for " 47L60"

showing 3 items of 3 documents

Bounded elements in certain topological partial *-algebras

2011

We continue our study of topological partial *algebras, focusing our attention to the interplay between the various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link between the strong and the weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial *algebras, emphasizing the crucial role played by appropriate bounded elements, called $\M$-bounded. Finally, some remarks are made concerning representations in terms of the so-called partial GC*-algebras of operators.

Pure mathematicsGeneral MathematicsBounded elementMathematics - Rings and AlgebrasPrimary 47L60 Secondary 46H15Topologypartial *-algebrasAlgebraRings and Algebras (math.RA)Settore MAT/05 - Analisi MatematicaBounded functionFOS: Mathematicsbounded elementsSpecial caseInvariant (mathematics)Mathematics
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Locally convex quasi C*-algebras and noncommutative integration

2015

In this paper 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 and we focus our attention on the so-called {\em locally convex quasi C*-algebras}. We show, in particular, that any strongly *-semisimple locally convex quasi C*-algebra $(\X,\Ao)$, can be represented in a class of noncommutative local $L^2$-spaces.

Pure mathematicsClass (set theory)Series (mathematics)General Mathematicsnoncommutative integrationRegular polygonFOS: Physical sciencesMathematical Physics (math-ph)Noncommutative geometrySettore MAT/05 - Analisi MatematicaNorm (mathematics)quasi C*-algebrasPrimary 46L08 Secondary 46L51 47L60Focus (optics)Mathematical PhysicsMathematics
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Fully representable and*-semisimple topological partial*-algebras

2012

We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome …

Discrete mathematics*-semisimple partial *-algebrasPure mathematicsbounded elements.*-semisimple partial *-algebraGeneral MathematicsMathematics - Rings and AlgebrasTopology08A55 46K05 46K10 47L60bounded elements}topological partial *-algebrasRings and Algebras (math.RA)Settore MAT/05 - Analisi MatematicaBounded functionFOS: MathematicsInvariant (mathematics)topological partial *-algebraMathematicsStudia Mathematica
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