Symmetric Strong Diameter Two Property View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04

AUTHORS

Rainis Haller, Johann Langemets, Vegard Lima, Rihhard Nadel

ABSTRACT

We study Banach spaces with the property that, given a finite number of slices of the unit ball, there exists a direction such that all these slices contain a line segment of length almost 2 in this direction. This property was recently named the symmetric strong diameter two property by Abrahamsen, Nygaard, and Põldvere. The symmetric strong diameter two property is not just formally stronger than the strong diameter two property (finite convex combinations of slices have diameter 2). We show that the symmetric strong diameter two property is only preserved by ℓ∞-sums, and working with weak star slices we show that Lip0(M) have the weak star version of the property for several classes of metric spaces M. More... »

PAGES

35

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00009-019-1306-1

DOI

http://dx.doi.org/10.1007/s00009-019-1306-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112433500


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