Search results for "Operator algebra"

showing 10 items of 89 documents

THE CAUCHY DUAL AND 2-ISOMETRIC LIFTINGS OF CONCAVE OPERATORS

2018

We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal. In particular, the quasinormality of compressions of such operators is studied.

Cauchy dual operatorsubnormal operatorPure mathematics[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]01 natural sciencessymbols.namesakeFOS: Mathematics0101 mathematicsconcave operatorMathematics47A05 47A15 47A20 47A63Mathematics::Functional AnalysisMathematics::Operator AlgebrasApplied Mathematics010102 general mathematicsHilbert spaceCauchy distributionExtension (predicate logic)Special class2-isometric liftingsA-contractionFunctional Analysis (math.FA)Dual (category theory)Mathematics - Functional Analysis010101 applied mathematicssymbolsAnalysis
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Induced and reduced unbounded operator algebras

2012

The induction and reduction precesses of an O*-vector space \({{\mathfrak M}}\) obtained by means of a projection taken, respectively, in \({{\mathfrak M}}\) itself or in its weak bounded commutant \({{\mathfrak M}^\prime_{\rm w}}\) are studied. In the case where \({{\mathfrak M}}\) is a partial GW*-algebra, sufficient conditions are given for the induced and the reduced spaces to be partial GW*-algebras again.

Unbounded operatorDiscrete mathematicsReduction (recursion theory)Applied MathematicsMathematics - Operator AlgebrasFOS: Physical sciencesMathematical Physics (math-ph)Space (mathematics)Centralizer and normalizerPrime (order theory)CombinatoricsProjection (relational algebra)Bounded functionInduced representationreduced representation: unbounded operator algebrasFOS: MathematicsOperator Algebras (math.OA)Mathematics::Representation TheoryMathematical PhysicsMathematics
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On the Rational Homogeneous Manifold Structure of the Similarity Orbits of Jordan Elements in Operator Algebras

1991

Considering a topological algebra B with unit e, an open group of invertible elements B −1 and continuous inversion (e. g. B = Banach algebra, B = C∞(Ω, M n (ℂ)) (Ω smooth manifold), B = special algebras of pseudo-differential operators), we are going to define the set of Jordan elements J ⊂ B (such that J = Set of Jordan operators if B = L(H), H Hilbert space) and to construct rational local cross sections for the operation mapping $$ {B^{ - 1}} \mathrel\backepsilon g \mapsto gJ{g^{ - 1}} $$ of B −1 on the similarity orbit S(J):= {gJg −1: g Є B −1}, J Є J.

Pure mathematicsJordan algebraTopological algebraInvariant manifoldHilbert spacelaw.inventionAlgebrasymbols.namesakeInvertible matrixOperator algebralawBanach algebrasymbolsUnit (ring theory)Mathematics
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Factorization in closed string field theory

1994

Abstract The so long made assumption, that a general closed-string vertex operator V should be built as a product of left- and right-moving vertex operators, rests on the fact that the closed-string Fock spce is constructed as a tensor product of left- and right-moving open-string Fock spaces. In this letter we will relax this assumption by proving that factorization of closed-string vertices is a general rule.

PhysicsNuclear and High Energy PhysicsPure mathematicsFísicaString field theoryFock spaceVertex (geometry)High Energy Physics::TheoryTensor productOperator (computer programming)Operator algebraFactorizationQuantum mechanicsProduct (mathematics)General Theoretical PhysicsPhysics Letters B
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Current Algebras as Hilbert Space Operator Cocycles

1994

Aspects of a generalized representation theory of current algebras in 3 + 1 dimensions axe discussed. Rules for a systematic computation of vacuum expectation values of products of currents are described. Their relation to gauge group actions in bundles of fermionic Fock spaces and to the sesquilinear form approach of Langmann and Ruijsenaars is explained. The regularization for a construction of an operator cocycle representation of the current algebra is explained. An alternative formula for the Schwinger terms defining gauge group extensions is written in terms of Wodzicki residue and Dixmier trace.

Algebrasymbols.namesakeWeak operator topologyMathematics::Operator AlgebrasSesquilinear formCurrent algebraHilbert spacesymbolsUnitary operatorNest algebraCompact operatorRepresentation theoryMathematics
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Decompositions and asymptotic limit for bicontractions

2012

The asymptotic limit of a bicontraction T (that is, a pair of commuting contractions) on a Hilbert space H is used to describe a Nagy–Foias–Langer type decomposition of T. This decomposition is refined in the case when the asymptotic limit of T is an orthogonal projection. The case of a bicontraction T consisting of hyponormal (even quasinormal) contractions is also considered, where we have ST∗=S2T∗.

Mathematics::Functional Analysissymbols.namesakeMathematics::Operator AlgebrasGeneral MathematicsMathematical analysisOrthographic projectionHilbert spacesymbolsLimit (mathematics)Mathematics::Spectral TheoryType (model theory)Mathematics
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The algebraic structure of cohomological field theory

1993

Abstract The algebraic foundation of cohomological field theory is presented. It is shown that these theories are based upon realizations of an algebra which contains operators for both BRST and vector supersymmetry. Through a localization of this algebra, we construct a theory of cohomological gravity in arbitrary dimensions. The observables in the theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach, different moduli spaces are obtained by introducing curvature si…

Pure mathematicsTopological quantum field theoryDifferential formAlgebraic structureGeneral Physics and AstronomyCodimensionModuli spaceAlgebraOperator algebraQuantum gravityGeometry and TopologyOperator product expansionMathematical PhysicsGeneral Theoretical PhysicsMathematics
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Symmetrization for singular semilinear elliptic equations

2012

In this paper, we prove some comparison results for the solution to a Dirichlet problem associated with a singular elliptic equation and we study how the summability of such a solution varies depending on the summability of the datum f. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.

Dirichlet problemSharp a priori estimatesSemilinear elliptic equationsMathematics::Operator AlgebrasApplied MathematicsMathematical analysisMathematics::Classical Analysis and ODEsMathematics::Analysis of PDEsComparison resultsSymmetrizationGeodetic datumElliptic curveSettore MAT/05 - Analisi MatematicaMathematics::K-Theory and HomologySymmetrizationMathematics
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Weyl symbols and boundedness of Toeplitz operators

2019

International audience; We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.

Mathematics::Functional AnalysisMathematics - Complex VariablesMathematics::Operator AlgebrasGeneral Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEs32U05 32W25 35S30 47B3501 natural sciencesToeplitz matrixFunctional Analysis (math.FA)AlgebraMathematics - Functional AnalysisFOS: MathematicsComputer Science::Symbolic Computation0101 mathematicsComplex Variables (math.CV)[MATH]Mathematics [math]Mathematics
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Closedness and lower semicontinuity of positive sesquilinear forms

2009

The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsMathematics::Operator AlgebrasSesquilinear formGeneral MathematicsMathematics::Optimization and ControlMathematics::General TopologyClosedness Semicontinuity Sesquilinear formsDomain (mathematical analysis)Topological vector spaceSettore MAT/05 - Analisi MatematicaAlgebra over a fieldCompleteness (statistics)Equivalence (measure theory)Subspace topologyQuotientMathematicsRendiconti del Circolo Matematico di Palermo
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