0000000000644673

AUTHOR

André Martiny

showing 3 related works from this author

Daugavet- and delta-points in Banach spaces with unconditional bases

2020

We study the existence of Daugavet- and delta-points in the unit sphere of Banach spaces with a 1 1 -unconditional basis. A norm one element x x in a Banach space is a Daugavet-point (resp. delta-point) if every element in the unit ball (resp. x x itself) is in the closed convex hull of unit ball elements that are almost at distance 2 2 from x x . A Banach space has the Daugavet property (resp. diametral local diameter two property) if and only if every norm one element is a Daugavet-point (resp. delta-point). It is well-known that a Banach space with the Daugavet property does not have an unconditional basis. Similarly spaces with the diametral local diameter two property do not have an un…

Convex hullUnit spherePure mathematicsMathematics::Functional AnalysisProperty (philosophy)Basis (linear algebra)010102 general mathematics05 social sciencesMathematicsofComputing_GENERALBanach spaceGeneral MedicineVDP::Matematikk og Naturvitenskap: 400::Matematikk: 41001 natural sciences46B20 (Primary) 46B22 46B04 (Secondary)Functional Analysis (math.FA)Mathematics - Functional AnalysisNorm (mathematics)0502 economics and businessFOS: Mathematics050207 economics0101 mathematicsElement (category theory)Constant (mathematics)Mathematics
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Two properties of Müntz spaces

2017

Abstract We show that Müntz spaces, as subspaces of C[0, 1], contain asymptotically isometric copies of c0 and that their dual spaces are octahedral.

Asymptotically isometric copy of c0General Mathematicslcsh:Mathematics010102 general mathematicsMuntz metallcsh:QA1-93901 natural sciences010101 applied mathematicsMüntz spaceDiameter 2 propertiesCalculusPhysics::Atomic and Molecular ClustersOctahedral space0101 mathematicsMathematicsDemonstratio Mathematica
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Asymptotic geometry and Delta-points

2022

We study Daugavet- and $\Delta$-points in Banach spaces. A norm one element $x$ is a Daugavet-point (respectively a $\Delta$-point) if in every slice of the unit ball (respectively in every slice of the unit ball containing $x$) you can find another element of distance as close to $2$ from $x$ as desired. In this paper we look for criteria and properties ensuring that a norm one element is not a Daugavet- or $\Delta$-point. We show that asymptotically uniformly smooth spaces and reflexive asymptotically uniformly convex spaces do not contain $\Delta$-points. We also show that the same conclusion holds true for the James tree space as well as for its predual. Finally we prove that there exis…

Mathematics - Functional Analysis46B20 46B22 46B04 46B06 (Primary)Mathematics::Functional AnalysisAlgebra and Number TheoryFOS: MathematicsVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410AnalysisFunctional Analysis (math.FA)Banach Journal of Mathematical Analysis
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