Search results for "C*-algebras"

showing 10 items of 37 documents

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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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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Completely positive invariant conjugate-bilinear maps on partial *-algebras

2007

The notion of completely positive invariant conjugate-bilinear map in a partial *-algebra is introduced and a generalized Stinespring theorem is proven. Applications to the existence of integrable extensions of *-representations of commutative, locally convex quasi*-algebras are also discussed.

Pure mathematicsIntegrable systemApplied MathematicsRegular polygonFOS: Physical sciencesBilinear interpolationMathematical Physics (math-ph)Completely positive mapSettore MAT/05 - Analisi MatematicaPartial O*-algebrasPartial *-algebraInvariant (mathematics)Commutative propertySettore MAT/07 - Fisica MatematicaAnalysisMathematical PhysicsConjugateMathematics
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Banach partial *-algebras: an overview

2019

A Banach partial $*$-algebra is a locally convex partial $*$-algebra whose total space is a Banach space. A Banach partial $*$-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of these objects and display a number of examples, namely, $L^p$-like function spaces and spaces of operators on Hilbert scales or lattices. Finally we analyze the important cases of Banach quasi $*$-algebras and $CQ^*$-algebras.

Pure mathematicsMathematics::Functional AnalysisAlgebra and Number Theorypartial inner product spacesPartial *-algebra Banach partial *-algebra CQ*-algebra partial inner product space operators on Hilbert scale.Partial algebraPartial *-algebraspartial $*$-algebraCQ*-algebraspartial inner product spaceSettore MAT/05 - Analisi Matematica$CQ^*$-algebraBanach partial *-algebrasoperators on Hilbert scaleBanach partial $*$-algebra46J1008A55Analysis47L60Mathematics
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Some classes of quasi *-algebras

2022

In this paper we will continue the analysis undertaken in [1] and in [2] [20] our investigation on the structure of Quasi-local quasi *-algebras possessing a sufficient family of bounded positive tracial sesquilinear forms. In this paper it is shown that any Quasi-local quasi *-algebras (A, A0), possessing a ”sufficient state” can be represented as non-commutative L2- spaces.

Quasi *-algebras Non-commutative L2-spacesSettore MAT/05 - Analisi MatematicaGeneral Mathematics
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Representations and derivations of quasi ∗-algebras induced by local modifications of states

2009

Abstract The relationship between the GNS representations associated to states on a quasi ∗-algebra, which are local modifications of each other (in a sense which we will discuss) is examined. The role of local modifications on the spatiality of the corresponding induced derivations describing the dynamics of a given quantum system with infinite degrees of freedom is discussed.

Quasi *-algebrasPure mathematicsApplied MathematicsQuantum dynamicsDegrees of freedomAlgebras of unbounded operatorsDerivationsRepresentationSettore MAT/05 - Analisi MatematicaQuantum systemDerivationQuantum dynamicsRepresentation (mathematics)Settore MAT/07 - Fisica MatematicaAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Representations of Quasi–local quasi *–algebras and non–commutative integration

2013

In this paper we are going to continue the analysis undertaken in [1] and [2] about the investigation on Quasi-local quasi *-algebras and their structure. Our aim is to show that any *-semisimple Quasi-local quasi *-algebra (A,A0) can be represented as a class of non-commutative L1-spaces.

Quasi *-algebrasSettore MAT/05 - Analisi Matematica
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Quasi-local quasi -algebras of measurable operators

2011

In this paper we will continue the analysis undertaken in [1] and in [2] our investigation on the structure of Quasi-local quasi *-algebras. In this paper it is shown that any Quasi-local quasi -algebras (A;A_0), can be represented as a class of Banach C-modules called CQ-algebra of measurable operators in Segal's sense.

Quasi-local quasi -algebrasSettore MAT/05 - Analisi Matematica
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C*-seminorms and representation on partial *-algebras

2008

In this paper we investigate the *-representations of a partial *-algebra A. In particular, it is proved that, if A is semiassociative and if the set of right multipliers is dense with respect to a seminorm p on A, there exists a bounded and regular *-represenation on A.

Settore MAT/05 - Analisi Matematica*-representations partial *-algebras
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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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