Search results for "Mathematics::Functional Analysis"

showing 10 items of 236 documents

Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions

2017

Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.

Discrete mathematicsMathematics::Functional AnalysisApplied MathematicsTopological tensor product010102 general mathematicsEberlein–Šmulian theoremWeakly compact operatorBloch type spaceBanach manifoldFinite-rank operator01 natural sciences010101 applied mathematicsEssential normWeighted spaces of analytic functionsFréchet spaceWeighted composition operatorInterpolation spaceBirnbaum–Orlicz space0101 mathematicsLp spaceAnalysisMathematics
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The Bishop–Phelps–Bollobás property for operators from c0 into some Banach spaces

2017

Abstract We exhibit a new class of Banach spaces Y such that the pair ( c 0 , Y ) has the Bishop–Phelps–Bollobas property for operators. This class contains uniformly convex Banach spaces and spaces with the property β of Lindenstrauss. We also provide new examples of spaces in this class.

Discrete mathematicsMathematics::Functional AnalysisApproximation propertyApplied Mathematics010102 general mathematicsEberlein–Šmulian theoremBanach spaceUniformly convex spaceBanach manifoldFinite-rank operator01 natural sciences010101 applied mathematicsCombinatoricsInterpolation space0101 mathematicsLp spaceAnalysisMathematicsJournal of Mathematical Analysis and Applications
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The Fixed Point Property in Banach Spaces with the NUS-Property

1997

Abstract In this paper, we show that the weak nearly uniform smooth Banach spaces have the fixed point property for nonexpansive mappings.

Discrete mathematicsMathematics::Functional AnalysisApproximation propertyApplied MathematicsEberlein–Šmulian theoremMathematics::Optimization and ControlBanach spaceBanach manifoldFixed-point propertyOpial propertyInterpolation spaceLp spaceAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Fixed point theory for a class of generalized nonexpansive mappings

2011

AbstractIn this paper we introduce two new classes of generalized nonexpansive mapping and we study both the existence of fixed points and their asymptotic behavior.

Discrete mathematicsMathematics::Functional AnalysisClass (set theory)Nonexpansive mappingApplied MathematicsMathematics::Optimization and ControlFixed-point theoremFixed pointFixed pointAnalysisDemiclosedness principleMathematicsJournal of Mathematical Analysis and Applications
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A unified Pietsch domination theorem

2008

In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.

Discrete mathematicsMathematics::Functional AnalysisDomination analysisApplied MathematicsLinear operatorsBanach spacePietsch domination theoremFunctional Analysis (math.FA)Linear mapMathematics - Functional AnalysisBanach spacesFOS: MathematicsIdeal (order theory)Algebraic numberAbsolutely summing mappingsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Finitely randomized dyadic systems and BMO on metric measure spaces

2015

Abstract We study the connection between BMO and dyadic BMO in metric measure spaces using finitely randomized dyadic systems, and give a Garnett–Jones type proof for a theorem of Uchiyama on a construction of certain BMO functions. We obtain a relation between the BMO norm of a suitable expectation over dyadic systems and the dyadic BMO norms of the original functions in different systems. The expectation is taken over only finitely randomized dyadic systems to overcome certain measurability questions. Applying our result, we derive Uchiyama’s theorem from its dyadic counterpart, which we also prove.

Discrete mathematicsMathematics::Functional AnalysisDyadic cubeApplied Mathematicsta111Mathematics::Analysis of PDEsMathematics::Classical Analysis and ODEsMetric measure spaceBounded mean oscillationQuantitative Biology::OtherBounded mean oscillationRandomized dyadic systemMetric spaceNorm (mathematics)Dyadic BMOAnalysisMathematicsNonlinear Analysis: Theory, Methods & Applications
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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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Boundaries for algebras of analytic functions on function module Banach spaces

2013

We consider the uniform algebra of continuous and bounded functions that are analytic on the interior of the closed unit ball of a complex Banach function module X. We focus on norming subsets of , i.e., boundaries, for such algebra. In particular, if X is a dual complex Banach space whose centralizer is infinite-dimensional, then the intersection of all closed boundaries is empty. This also holds in case that X is an -sum of infinitely many Banach spaces and further, the torus is a boundary.

Discrete mathematicsMathematics::Functional AnalysisGeneral MathematicsUniform algebraSpectrum (functional analysis)Interpolation spaceFinite-rank operatorBanach manifoldInfinite-dimensional holomorphyC0-semigroupLp spaceMathematicsMathematische Nachrichten
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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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