Search results for "Continuous functions on a compact Hausdorff space"

showing 6 items of 6 documents

Norm or numerical radius attaining polynomials on C(K)

2004

Abstract Let C(K, C ) be the Banach space of all complex-valued continuous functions on a compact Hausdorff space K. We study when the following statement holds: every norm attaining n-homogeneous complex polynomial on C(K, C ) attains its norm at extreme points. We prove that this property is true whenever K is a compact Hausdorff space of dimension less than or equal to one. In the case of a compact metric space a characterization is obtained. As a consequence we show that, for a scattered compact Hausdorff space K, every continuous n-homogeneous complex polynomial on C(K, C ) can be approximated by norm attaining ones at extreme points and also that the set of all extreme points of the u…

Applied MathematicsMathematical analysisBanach spaceHausdorff spaceContinuous functions on a compact Hausdorff spaceCombinatoricsMetric spacesymbols.namesakeUniform normNorm (mathematics)Hausdorff dimensionsymbolsStone–Weierstrass theoremAnalysisMathematicsJournal of Mathematical Analysis and Applications
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A Note on Locally ??-compact Spaces

1995

: The local version of the concept of ℰτ-compactness (where ℰ is a class of Hausdorff spaces and ℰ is a cardinal) introduced by the first author as a generalization of Her-rlich's concept of ℰ-compactness (and hence, also of Mrowka's E-compactness) is defined and the corresponding theory is initiated. An essential part of the theory is developed under the additional assumption that all spaces from ℰ are absolute extensors for spaces under consideration. The theory contains as a special case the classical theory of local compactness.

Class (set theory)Pure mathematicsRiesz–Markov–Kakutani representation theoremGeneral NeuroscienceVague topologyHausdorff spaceMathematics::General TopologyLocally compact groupContinuous functions on a compact Hausdorff spaceGeneral Biochemistry Genetics and Molecular BiologyCompact spaceHistory and Philosophy of ScienceRelatively compact subspaceMathematicsAnnals of the New York Academy of Sciences
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Connected components in the space of composition operators onH∞ functions of many variables

2003

LetE be a complex Banach space with open unit ballBe. The structure of the space of composition operators on the Banach algebra H∞, of bounded analytic functions onBe with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly insideBe form a path connected component. WhenE is a Hilbert space or aCo(X)- space, the path connected components are shown to be the open balls of radius 2.

Discrete mathematicsAlgebra and Number TheoryApproximation propertyInfinite-dimensional vector functionHilbert spaceOperator theoryOperator spaceContinuous functions on a compact Hausdorff spacesymbols.namesakeOperator algebraBanach algebrasymbolsAnalysisMathematicsIntegral Equations and Operator Theory
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A space of projections on the Bergman space

2010

We define a set of projections on the Bergman space A 2 , which is parameterized by an ane subset of a Banach space of holomorphic functions in the disk and which includes the classical Forelli-Rudin projections.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsMathematics::Complex VariablesGeneral MathematicsInfinite-dimensional vector functionHolomorphic functionBanach spaceMathematics::General TopologyQuotient space (linear algebra)Continuous functions on a compact Hausdorff spaceBergman spaceBesov spaceBergman kernelMathematicsAnnales Academiae Scientiarum Fennicae Mathematica
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Transformations by diagonal matrices in a normed space

1962

Discrete mathematicsStrictly convex spaceComputational MathematicsNormed algebraBs spaceApplied MathematicsVanish at infinityPseudometric spaceContinuous functions on a compact Hausdorff spaceDual normMathematicsNormed vector spaceNumerische Mathematik
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Representing compact sets of compact operators and of compact range vector measures

1987

symbols.namesakeApproximation propertyNuclear operatorGeneral MathematicsHilbert spacesymbolsFinite-rank operatorCompact operatorTopologyInvariant subspace problemContinuous functions on a compact Hausdorff spaceCompact operator on Hilbert spaceMathematicsArchiv der Mathematik
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