Search results for "Theorem"

showing 10 items of 1250 documents

On generalized a-Browder's theorem

2007

We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0(�I T) asbelongs to certain sets of C. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators. 1. Preliminaries. Let L(X) denote the space of bounded linear oper- ators on an infinite-dimensional complex Banach space X. For T ∈ L(X), denote by α(T) the dimension of the kernel ker T, and by β(T) the codi- mension of the range T(X). The operator T ∈ L(X) is called upper semi- Fredholm if α(T) < ∞ and T(X) is closed, and lower …

Discrete mathematicsMathematics::Functional AnalysisFredholm theoryMathematics::Operator AlgebrasGeneral MathematicsFredholm operatorgeneralized Browder's theoremBanach spaceMathematics::Spectral TheoryFredholm theorySVEPCombinatoricssymbols.namesakeKernel (algebra)Operator (computer programming)Mathematics Subject ClassificationIntegerSettore MAT/05 - Analisi MatematicaMathematics::K-Theory and HomologyBounded functionsymbolsgeneralized Weyl's theoremMathematicsStudia Mathematica
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Injective spaces of real-valued functions with the baire property

1995

Generalizing the technique used by S.A. Argyros in [3], we give a lemma from which certain Banach spaces are shown to be non-injective. This is applied mainly to study the injectivity of spaces of real-valued Borel functions and functions with the Baire property on a topological space. The results obtained in this way do not follow from previous works about this matter.

Discrete mathematicsMathematics::Functional AnalysisFréchet spaceGeneral MathematicsTopological tensor productMathematics::General TopologyInterpolation spaceBaire category theoremOpen mapping theorem (functional analysis)Baire measureTopological vector spaceComplete metric spaceMathematicsIsrael Journal of Mathematics
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A Mönch type fixed point theorem under the interior condition

2009

Abstract In this paper we show that the well-known Monch fixed point theorem for non-self mappings remains valid if we replace the Leray–Schauder boundary condition by the interior condition. As a consequence, we obtain a partial generalization of Petryshyn's result for nonexpansive mappings.

Discrete mathematicsMathematics::Functional AnalysisGeneralizationApplied MathematicsInterior conditionMathematics::Analysis of PDEsBanach spaceFixed-point theoremType (model theory)Mönch fixed point theoremBanach spacesStrictly star-shaped setLeray–Schauder conditionBoundary value problemAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Strict u-ideals in Banach spaces

2009

We study strict u-ideals in Banach spaces. A Banach space X is a strict u-ideal in its bidual when the canonical decomposition X = X X ? is unconditional. We characterize Banach spaces which are strict u-ideals in their bidual and show that if X is a strict u-ideal in a Banach space Y then X contains c0. We also show that '1 is not a u-ideal.

Discrete mathematicsMathematics::Functional AnalysisMathematics::Commutative AlgebraApproximation propertyGeneral MathematicsEberlein–Šmulian theoremInfinite-dimensional vector functionBanach spaceInterpolation spaceBanach manifoldC0-semigroupLp spaceMathematicsStudia Mathematica
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Entire Functions of Bounded Type on Fréchet Spaces

1993

We show that holomorphic mappings of bounded type defined on Frechet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem.

Discrete mathematicsMathematics::Functional AnalysisMathematics::Complex VariablesGeneral MathematicsBounded functionUniform boundednessBounded deformationInfinite-dimensional holomorphyBounded inverse theoremIdentity theoremExponential typeBounded operatorMathematicsMathematische Nachrichten
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Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets

2013

We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. We provide a metric area formula that applies to these mappings and more generally to all almost everywhere metrically differentiable Lipschitz mappings defined on a Carnot group. peerReviewed

Discrete mathematicsMathematics::Functional AnalysisProperty (philosophy)General Mathematicsmetric area formulata111Mathematics::Analysis of PDEsCarnot groupBanach homogeneous groupsalmost everywhere differentiabilityRadon-Nikodym propertyLipschitz continuityRadon–Nikodym theoremBanach homogeneous groups; metric area formula; almost everywhere differentiability; Radon-Nikodym propertyMetric (mathematics)Homogeneous groupMathematics::Metric GeometryAlmost everywhereDifferentiable functionMathematics
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Henstock–Kurzweil–Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space

2013

Abstract The aim of this paper is to describe Henstock–Kurzweil–Pettis (HKP) integrable compact valued multifunctions. Such characterizations are known in case of functions (see Di Piazza and Musial (2006)  [16] ). It is also known (see Di Piazza and Musial (2010)  [19] ) that each HKP-integrable compact valued multifunction can be represented as a sum of a Pettis integrable multifunction and of an HKP-integrable function. Invoking to that decomposition, we present a pure topological characterization of integrability. Having applied the above results, we obtain two convergence theorems, that generalize results known for HKP-integrable functions. We emphasize also the special role played in …

Discrete mathematicsMathematics::Functional AnalysisProperty (philosophy)Henstock integralIntegrable systemApplied MathematicsBanach spaceconvergence theoremsFunction (mathematics)Characterization (mathematics)set-valued Henstock-Kurzweil-Pettis integralset-valued Pettis integralsupport functionMultifunctionSettore MAT/05 - Analisi MatematicaConvergence (routing)AnalysisselectorMathematicsJournal of Mathematical Analysis and Applications
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On the structure of the ultradistributions of Beurling type

2008

Let O be a nonempty open set of the k-dimensional euclidean space Rk. In this paper, we give a structure theorem on the ultradistributions of Beurling type in O. Also, other structure results on certain ultradistributions are obtained, in terms of complex Borel measures in O.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsAlgebra and Number TheoryEuclidean spaceRiesz–Markov–Kakutani representation theoremApplied MathematicsOpen setStructure (category theory)Banach spaceType (model theory)Computational MathematicsLocally convex topological vector spaceGeometry and TopologyAnalysisStructured program theoremMathematicsRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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Factorization of (q,p)-summing polynomials through Lorentz spaces

2017

[EN] We present a vector valued duality between factorable (q,p)-summing polynomials and (q,p)-summing linear operators on symmetric tensor products of Banach spaces. Several applications are provided. First, we prove a polynomial characterization of cotype of Banach spaces. We also give a variant of Pisier's factorization through Lorentz spaces of factorable (q,p)-summing polynomials from C(K)-spaces. Finally, we show a coincidence result for (q,p)-concave polynomials.(c) 2016 Elsevier Inc. All rights reserved.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsApplied MathematicsDiscrete orthogonal polynomials010102 general mathematicsBanach space010103 numerical & computational mathematics01 natural sciencesClassical orthogonal polynomialsDifference polynomialsFactorizationPisier's theoremWilson polynomialsOrthogonal polynomialsSymmetric tensorSumming polynomialsFactorization0101 mathematicsMATEMATICA APLICADAAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Property (M) and the weak fixed point property

1997

It is shown that in Banach spaces with the property (M) of Kalton, nonexpansive self mappings of nonempty weakly compact convex sets necessarily have fixed points. The stability of this conclusion under renormings is examined and conditions for such spaces to have weak normal structure are considered.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsApproximation propertyApplied MathematicsGeneral MathematicsTopological tensor productEberlein–Šmulian theoremBanach spaceUniformly convex spaceFixed-point propertyOpial propertyInterpolation spaceMathematicsProceedings of the American Mathematical Society
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