Strong Diameter Two Property and Convex Combinations of Slices Reaching the Unit Sphere

López Pérez, Ginés; Martín Suárez, Miguel; Rueda Zoca, Abraham

doi:10.1007/s00009-019-1403-1

pre2019_CCS_Sphere_reaching.pdf (356.7Kb)

Identificadores

URI: https://hdl.handle.net/10481/98336

DOI: 10.1007/s00009-019-1403-1

Exportar

Editorial

Springer Nature

Date

2019

Referencia bibliográfica

Published version: López-Pérez, G., Martín, M. & Rueda Zoca, A. Strong Diameter Two Property and Convex Combinations of Slices Reaching the Unit Sphere. Mediterr. J. Math. 16, 122 (2019). https://doi.org/10.1007/s00009-019-1403-1

Sponsorship

Spanish MINECO/FEDER MTM2015-65020-P; Junta de Andalucía/FEDER FQM-185

Abstract

We characterise the class of those Banach spaces in which every convex combination of slices of the unit ball intersects the unit sphere as the class of those spaces in which every convex combination of slices of the unit ball contains two points at distance exactly two. Also, we study when the convex combinations of slices of the unit ball are relatively open or have non-empty relative interior for different topologies, studying the relationship between them and studying these properties for L∞-spaces and preduals of L1-spaces

Collections

DAM - Artículos

Except where otherwise noted, this item's license is described as Attribution-NoDerivatives 4.0 Internacional