Strong Diameter Two Property and Convex Combinations of Slices Reaching the Unit Sphere
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Show full item recordEditorial
Springer Nature
Date
2019Referencia 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-185Abstract
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