Search results for "Cone absolutely summing operator"

showing 3 items of 3 documents

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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On set-valued cone absolutely summing maps

2009

Spaces of cone absolutely summing maps are generalizations of Bochner spaces Lp(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) , and to derive necessary and sufficient conditions for a set-valued map to be such a set-valued cone absolutely summing map. We …

Discrete mathematicsGeneral MathematicsBanach spaceBochner spaceSpace (mathematics)Measure (mathematics)Separable spaceCombinatoricsBanach lattice Bochner space Cone absolutely summing operator Integrably bounded set-valued function Set-valued operatorNumber theoryCone (topology)Settore MAT/05 - Analisi MatematicaBounded functionMathematicsCentral European Journal of Mathematics
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On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts

2011

The aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the R ̊adstr ̈om embedding theorem.

Pettis integralSet (abstract data type)Mathematics::Functional AnalysisPure mathematicsIntegrable systemBounded functionBanach latticeBochner integralBanach spaceEmbeddingAbsolutely summing operator Banach lattice Bochner integral Pettis integral cone absolutely summing operator integrably bounded set- valued function set-valued operator.Mathematics
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