6533b839fe1ef96bd12a65cd
RESEARCH PRODUCT
Asymptotic geometry and Delta-points
Trond A. AbrahamsenVegard LimaAndré MartinyYoël Perreausubject
Mathematics - Functional Analysis46B20 46B22 46B04 46B06 (Primary)Mathematics::Functional AnalysisAlgebra and Number TheoryFOS: MathematicsVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410AnalysisFunctional Analysis (math.FA)description
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 exists a superreflexive Banach space with a Daugavet- or $\Delta$-point provided there exists such a space satisfying a weaker condition.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-01-01 | Banach Journal of Mathematical Analysis |