6533b85bfe1ef96bd12bbf08

RESEARCH PRODUCT

On Daugavet indices of thickness

Rihhard NadelAbraham Rueda ZocaVegard LimaRainis HallerJohann Langemets

subject

Unit spherePure mathematicsMathematics::Functional AnalysisIndex (economics)Existential quantificationOpen problem010102 general mathematicsRegular polygonBanach space01 natural sciencesInfimum and supremumFunctional Analysis (math.FA)Negative - answerMathematics - Functional Analysis0103 physical sciencesFOS: Mathematics46B20 46B22010307 mathematical physics0101 mathematicsAnalysisMathematics

description

Inspired by R. Whitley's thickness index the last named author recently introduced the Daugavet index of thickness of Banach spaces. We continue the investigation of the behavior of this index and also consider two new versions of the Daugavet index of thickness, which helps us solve an open problem which connect the Daugavet indices with the Daugavet equation. Moreover, we will improve the formerly known estimates of the behavior of Daugavet index on direct sums of Banach spaces by establishing sharp bounds. As a consequence of our results we prove that, for every $0<\delta<2$, there exists a Banach space where the infimum of the diameter of convex combinations of slices of the unit ball is exactly $\delta$, solving an open question from the literature. Finally, we prove that an open question posed by Ivakhno in 2006 about the relation between the radius and diameter of slices has a negative answer.

yearjournalcountryeditionlanguage
2020-05-05
http://arxiv.org/abs/2005.02045