Search results for "bounded elements."

showing 6 items of 6 documents

Bounded elements of C*-inductive locally convex spaces

2013

The notion of bounded element of C*-inductive locally convex spaces (or C*-inductive partial *-algebras) is introduced and discussed in two ways: The first one takes into account the inductive structure provided by certain families of C*-algebras; the second one is linked to the natural order of these spaces. A particular attention is devoted to the relevant instance provided by the space of continuous linear maps acting in a rigged Hilbert space.

Discrete mathematicsPositive elementApplied Mathematics010102 general mathematicsMathematics - Operator AlgebrasRigged Hilbert spaceMathematics - Rings and AlgebrasLF-spaceSpace (mathematics)01 natural sciencesOperator spaceBounded operatorBounded elements Inductive limit of C*-algebras Partial *-algebras010101 applied mathematics47L60 47L40Rings and Algebras (math.RA)Bounded functionLocally convex topological vector spaceFOS: Mathematics0101 mathematicsOperator Algebras (math.OA)Mathematics
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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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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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Order bounded elements of topological *-algebras

2012

Several different notions of {\em bounded} element of a topological *-algebra $\A$ are considered. The case where boundedness is defined via the natural order of $\A$ is examined in more details and it is proved that under certain circumstances (in particular, when $\A$ possesses sufficiently many *-representations) {\em order boundedness} is equivalent to {\em spectral boundedness}.

Settore MAT/05 - Analisi MatematicaBounded elements Topological *-algebrasGeneral Medicine
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Banach elements and spectrum in Banach quasi *-algebras

2006

A normal Banach quasi -algebra (X;A_0) has a distinguished Banach - algebra X_b consisting of bounded elements of X. The latter -algebra is shown to coincide with the set of elements of X having fi nite spectral radius. If the family P(X) of bounded invariant positive sesquilinear forms on X contains suffi ciently many elements then the Banach -algebra of bounded elements can be characterized via a C -seminorm defi ned by the elements of P(X).

AlgebraPure mathematicsJordan algebraGeneral MathematicsBounded functionSpectrum (functional analysis)SubalgebraDivision algebraAlgebra representationbounded elements normed quasi *-algebrasCellular algebraUniversal enveloping algebraMathematics
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An overview on bounded elements in some partial algebraic structures

2015

The notion of bounded element is fundamental in the framework of the spectral theory. Before implanting a spectral theory in some algebraic or topological structure it is needed to establish which are its bounded elements. In this paper, we want to give an overview on bounded elements of some particular algebraic and topological structures, summarizing our most recent results on this matter.

Pure mathematicsEngineeringSpectral theorySettore MAT/05 - Analisi MatematicaAlgebraic structurebusiness.industryBounded functionStructure (category theory)Mechanical engineeringBounded elements (*-semisimple topological) partial *-algebras C*-inductive locally convex spacesAlgebraic numberElement (category theory)business
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