Search results for "PROPERTY"

showing 10 items of 955 documents

A note on banach partial *-algebras

2006

A Banach partial *-algebra is a locally convex partial *-algebra whose total space is a Banach space. A Banach partial *-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of such objects and display a number of examples, namely LP-like function spaces and spaces of operators on Hilbert scales.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsApproximation propertyGeneral MathematicsInfinite-dimensional vector functionEberlein–Šmulian theoremBanach spaceInterpolation spaceFinite-rank operatorBanach manifoldLp spaceMathematicsMediterranean Journal of Mathematics
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Bishop–Phelps–Bollobás property for certain spaces of operators

2014

Abstract We characterize the Banach spaces Y for which certain subspaces of operators from L 1 ( μ ) into Y have the Bishop–Phelps–Bollobas property in terms of a geometric property of Y , namely AHSP. This characterization applies to the spaces of compact and weakly compact operators. New examples of Banach spaces Y with AHSP are provided. We also obtain that certain ideals of Asplund operators satisfy the Bishop–Phelps–Bollobas property.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsFunctional analysisApproximation propertyApplied MathematicsBanach spaceCharacterization (mathematics)Operator theoryCompact operatorLinear subspaceCompact operator on Hilbert spaceAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Unconditional Basis and Gordon–Lewis Constants for Spaces of Polynomials

2001

Abstract No infinite dimensional Banach space X is known which has the property that for m ⩾2 the Banach space of all continuous m -homogeneous polynomials on X has an unconditional basis. Following a program originally initiated by Gordon and Lewis we study unconditionality in spaces of m -homogeneous polynomials and symmetric tensor products of order m in Banach spaces. We show that for each Banach space X which has a dual with an unconditional basis ( x * i ), the approximable (nuclear) m -homogeneous polynomials on X have an unconditional basis if and only if the monomial basis with respect to ( x * i ) is unconditional. Moreover, we determine an asymptotically correct estimate for the …

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsPolynomialBanach spacepolynomialBasis (linear algebra)Banach spaceMonomial basisunconditional basisUnconditional convergenceOrder (group theory)Interpolation spaceSymmetric tensorsymmetric tensor productGordon–Lewis propertyAnalysisMathematicsJournal of Functional Analysis
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Fredholm composition operators on algebras of analytic functions on Banach spaces

2010

AbstractWe prove that Fredholm composition operators acting on the uniform algebra H∞(BE) of bounded analytic functions on the open unit ball of a complex Banach space E with the approximation property are invertible and arise from analytic automorphisms of the ball.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsSpectral theoryApproximation propertyFredholm operatorGlobal analytic functionFinite-rank operatorFredholm integral equationFredholm operatorCompact operatorFredholm theorysymbols.namesakesymbolsComposition operatorBounded analytic functionAnalysisMathematicsJournal of Functional Analysis
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Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings

2006

Abstract It is shown that if the modulus Γ X of nearly uniform smoothness of a reflexive Banach space satisfies Γ X ′ ( 0 ) 1 , then every bounded closed convex subset of X has the fixed point property for nonexpansive mappings. In particular, uniformly nonsquare Banach spaces have this property since they are properly included in this class of spaces. This answers a long-standing question in the theory.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsUniformly nonsquare spacesApproximation propertyEberlein–Šmulian theoremBanach spaceNonexpansive mappingsUniformly convex spaceBanach manifoldFixed-point propertyNearly uniform smoothnessFixed pointsReflexive spaceLp spaceAnalysisMathematicsJournal of Functional Analysis
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Existence theorems for m-accretive operators in Banach spaces

2005

Abstract In 1985, the second author proved a surjective result for m -accretive and ϕ -expansive mappings for uniformly smooth Banach spaces. However, in this case, we have been able to remove the uniform smoothness of the Banach space, without any additional assumption.

Discrete mathematicsMathematics::Functional AnalysisZeros for m-accretive operatorsApproximation propertySurjectivityApplied MathematicsEberlein–Šmulian theoremAccretivityUniformly convex spaceBanach manifoldFinite-rank operatorInterpolation spaceOpen mapping theorem (functional analysis)Lp spaceAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Compactness of time-frequency localization operators on L2(Rd)

2006

Abstract In this paper, we consider localization operators on L 2 ( R d ) defined by symbols in a subclass of the modulation space M ∞ ( R 2 d ) . We show that these operators are compact and that this subclass is “optimal” for compactness.

Discrete mathematicsModulation spaceCompact operatorApproximation propertyShort-time Fourier transformModulation spaceLocalization operatorOperator theoryCompact operatorCompact operator on Hilbert spaceSubclassCompact spaceTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESShort-time Fourier transformAnalysisComputer Science::Formal Languages and Automata TheoryMathematicsJournal of Functional Analysis
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The fixed point property for mappings admitting a center

2007

Abstract We introduce a class of nonlinear continuous mappings in Banach spaces which allow us to characterize the Banach spaces without noncompact flat parts in their spheres as those that have the fixed point property for this type of mapping. Later on, we give an application to the existence of zeroes for certain kinds of accretive operators.

Discrete mathematicsNonlinear systemClass (set theory)Applied MathematicsBanach spaceCenter (group theory)Fixed pointType (model theory)Fixed-point propertyAnalysisNonlinear operatorsMathematicsNonlinear Analysis: Theory, Methods & Applications
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Interpolation and approximation in L2(γ)

2007

Assume a standard Brownian motion W=(W"t)"t"@?"["0","1"], a Borel function f:R->R such that f(W"1)@?L"2, and the standard Gaussian measure @c on the real line. We characterize that f belongs to the Besov space B"2","q^@q(@c)@?(L"2(@c),D"1","2(@c))"@q","q, obtained via the real interpolation method, by the behavior of a"X(f(X"1);@t)@[email protected]?f(W"1)-P"X^@tf(W"1)@?"L"""2, where @t=(t"i)"i"="0^n is a deterministic time net and P"X^@t:L"2->L"2 the orthogonal projection onto a subspace of 'discrete' stochastic integrals x"[email protected]?"i"="1^nv"i"-"1(X"t"""i-X"t"""i"""-"""1) with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the…

Discrete mathematicsNumerical AnalysisHermite polynomialsGeneric propertyApplied MathematicsGeneral MathematicsLinear equation over a ringGaussian measuresymbols.namesakeWiener processsymbolsBesov spaceMartingale (probability theory)Real lineAnalysisMathematicsJournal of Approximation Theory
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Property (gab) through localized SVEP

2015

In this article we study the property (gab) for a bounded linear operator T 2 L(X) on a Banach space X which is a stronger variant of Browder's theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations. 2010 Mathematics Subject Classication. Primary 47A10, 47A11; Secondary 47A53, 47A55.

Discrete mathematicsNumerical AnalysisPure mathematicsControl and OptimizationSpectral theoryProperty (philosophy)Property (gab) local spectral subspaces Browder type theorems.Applied Mathematics010102 general mathematicsBanach space010103 numerical & computational mathematics01 natural sciencesStability (probability)Bounded operatorSettore MAT/05 - Analisi Matematica0101 mathematicsAnalysisMathematics
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