Search results for "Operator Algebra"

showing 9 items of 89 documents

Highly transitive actions of free products

2013

We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group $\PSL_2(\Z)\simeq (\Z/2\Z)*(\Z/3\Z)$ admits a faithful and highly transitive action on a countable set.

Transitive actionHighly transitive actionsMSC: Primary: 20B22 20E06Group Theory (math.GR)01 natural sciencesBaire category Theorem[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]CombinatoricsFree products0103 physical sciencesFOS: MathematicsCountable set0101 mathematics20B22MathematicsTransitive relation20E06Group (mathematics)Mathematics::Operator Algebras010102 general mathematics20E06 20B2216. Peace & justiceFree productBaire category theorem010307 mathematical physicsGeometry and TopologyMathematics - Group Theory
researchProduct

Unbounded derivations and *-automorphisms groups of Banach quasi *-algebras

2018

This paper is devoted to the study of unbounded derivations on Banach quasi *-algebras with a particular emphasis to the case when they are infinitesimal generators of one parameter automorphisms groups. Both of them, derivations and automorphisms are considered in a weak sense; i.e., with the use of a certain families of bounded sesquilinear forms. Conditions for a weak *-derivation to be the generator of a *-automorphisms group are given.

Unbounded derivationPure mathematicsAutomorphisms groups and their infinitesimal generatorsInfinitesimalBanach quasi *-algebra01 natural sciencesMathematics::Group Theory*-Automorphisms groups and their infinitesimal generatorSettore MAT/05 - Analisi Matematica0103 physical sciencesFOS: MathematicsAutomorphisms groups and their infinitesimal generators; Banach quasi; Integrability of derivation; Unbounded derivations; Automorphisms groups and their infinitesimal generators; Banach quasi; Integrability of derivation; Unbounded derivationsBanach quasi0101 mathematicsOperator Algebras (math.OA)MathematicsGroup (mathematics)Applied Mathematics010102 general mathematicsIntegrability of derivationMathematics - Operator AlgebrasAutomorphismUnbounded derivationsFunctional Analysis (math.FA)Mathematics - Functional AnalysisBounded function010307 mathematical physicsGenerator (mathematics)
researchProduct

Bicommutants of reduced unbounded operator algebras

2009

The unbounded bicommutant $(\mathfrak M_{E'})''$ of the {\em reduction} of an O*-algebra $\MM$ via a given projection $E'$ weakly commuting with $\mathfrak M$ is studied, with the aim of finding conditions under which the reduction of a GW*-algebra is a GW*-algebra itself. The obtained results are applied to the problem of the existence of conditional expectations on O*-algebras.

Unbounded operatorDiscrete mathematicsPure mathematicsReduction (recursion theory)Applied MathematicsGeneral MathematicsFOS: Physical sciencesMathematical Physics (math-ph)Conditional expectationProjection (linear algebra)Unbounded operator algebrasSettore MAT/05 - Analisi MatematicaAlgebra over a fieldBicommutantMathematical PhysicsMathematicsBicommutant
researchProduct

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
researchProduct

Pseudodifferential operators of Beurling type and the wave front set

2008

AbstractWe investigate the action of pseudodifferential operators of Beurling type on the wave front sets. More precisely, we show that these operators are microlocal, that is, preserve or reduce wave front sets. Some consequences on micro-hypoellipticity are derived.

WavefrontPseudodifferential operatorsMathematics::Complex VariablesMathematics::Operator AlgebrasApplied MathematicsMathematical analysisWave front setMicrolocal analysisMathematics::Analysis of PDEsPseudodifferential operatorWave front setType (model theory)Mathematics::Spectral TheoryAction (physics)Set (abstract data type)UltradistributionNonlinear Sciences::Pattern Formation and SolitonsAnalysisMathematicsFront (military)Journal of Mathematical Analysis and Applications
researchProduct

A note on Hilbert’s weak nullstellensatz

2015

In this article, through a suitable generalization of the well-known notion of spectrum of an element of an arbitrary normed algebra of Operator Theory, it will be possible to give another simple proof of the Hilbert’s Weak Nullstellensatz.

[MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC]lcsh:MathematicsSpectrum[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]lcsh:Descriptive and experimental mechanicsOperator algebraComputer Science::Computational GeometryComputer Science::Data Structures and Algorithmslcsh:QA1-939Ideallcsh:QC120-168.85
researchProduct

On Gelfand-Mazur Theorem

2015

From a suitable extension of the notion of spectrum drew from normed algebra theory, it will be possible, among other things, to provide some generalizations of the well-known Gelfand-Mazur theorem. In this brief research report, we wish to pursue one of these, as achieved in I,4.

[MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC]topology[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]Gelfand-Mazur theorem[MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA][MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA][MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA][MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA]ComputingMilieux_MISCELLANEOUSspectrum
researchProduct

Resolvent estimates for elliptic quadratic differential operators

2011

Sharp resolvent bounds for non-selfadjoint semiclassical elliptic quadratic differential operators are established, in the interior of the range of the associated quadratic symbol.

quadratic differential operatorSemiclassical physics47A10 35P05 15A63 53D2215A6353D22spectrumMathematics - Spectral TheoryMathematics - Analysis of PDEsQuadratic equationFOS: Mathematicsnonselfadjoint operator35P05Quadratic differentialSpectral Theory (math.SP)ResolventMathematicsNumerical AnalysisMathematics::Operator AlgebrasApplied MathematicsMathematical analysisSpectrum (functional analysis)resolvent estimateMathematics::Spectral TheoryDifferential operator47A10Range (mathematics)FBI-Bargmann transformAnalysisAnalysis of PDEs (math.AP)
researchProduct

Liftings and extensions of operators in Brownian setting

2020

We investigate the operators T on a Hilbert space H which have 2-isometric liftings S with the property S ∗ S H ⊂ H . We show that such liftings are closely related to some extensions of T, which h...

symbols.namesakePure mathematicsAlgebra and Number TheoryProperty (philosophy)Mathematics::Operator AlgebrasHilbert spacesymbols010103 numerical & computational mathematicsExtension (predicate logic)0101 mathematics01 natural sciencesBrownian motionMathematicsLinear and Multilinear Algebra
researchProduct