Search results for "Summing operator"

showing 3 items of 13 documents

On weakly measurable stochastic processes and absolutely summing operators

2006

A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered

Pettis integralSettore MAT/05 - Analisi MatematicaStochastic processGeneral MathematicsMathematical analysisApplied mathematicsPettis integral McShane integral amart uniform amart absolutely summing operatorsMathematicsMathematica Bohemica
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On $p$-Dunford integrable functions with values in Banach spaces

2018

[EN] Let (Omega, Sigma, mu) be a complete probability space, X a Banach space and 1 X. Special attention is paid to the compactness of the Dunford operator of f. We also study the p-Bochner integrability of the composition u o f: Omega->Y , where u is a p-summing operator from X to another Banach space Y . Finally, we also provide some tests of p-Dunford integrability by using w*-thick subsets of X¿.

Pure mathematicsMathematics::Functional AnalysisIntegrable systemApplied MathematicsOperator (physics)010102 general mathematicsP-Summing operatorw*-Thick setBanach space28B05 46G10Composition (combinatorics)01 natural sciencesP-Pettis integrable functionFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsDunford operatorCompact spaceProbability spaceP-Dunford integrable functionFOS: Mathematics0101 mathematicsMATEMATICA APLICADAAnalysisMathematics
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Operator martingale decomposition and the Radon-Nikodym property in Banach spaces

2010

Abstract We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon–Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney–Schaefer l-tensor product E ⊗ ˜ l Y , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon–Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on E ⊗ ˜ l Y . Secondly, we derive a Riesz decomposition for uniform …

Uniform amartPure mathematicsDinculeanu operatorApproximation propertyEberlein–Šmulian theoremBanach spaceRadon–Nikodým propertyFinite-rank operatorBanach manifoldBanach lattice Banach space Bochner norm Cone absolutely summing operator Convergent martingale Convergent submartingale Dinculeanu operator Radon–Nikodým propertySettore MAT/05 - Analisi MatematicaLp spaceC0-semigroupBanach lattice Banach space Bochner norm Cone absolutely summing operator Convergent martingale Convergent submartingale Dinculeanu operator Radon–Nikodým property Uniform amartMathematicsDiscrete mathematicsMathematics::Functional AnalysisBanach spaceApplied MathematicsConvergent martingaleConvergent submartingaleBanach latticeBochner normCone absolutely summing operatorBounded functionAnalysis
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