Extreme differences between weakly open subsets and convex combinations of slices in Banach spaces

Abraham Rueda Zoca; Gin\'es L\'opez-P\'erez; Julio Becerra Guerrero

REVIEW

Extreme differences between weakly open subsets and convex combinations of slices in Banach spaces

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1309.4950 v3 pith:PJCBIRXE submitted 2013-09-19 math.FA

Extreme differences between weakly open subsets and convex combinations of slices in Banach spaces

Julio Becerra Guerrero , Gin\'es L\'opez-P\'erez , Abraham Rueda Zoca This is my paper

classification math.FA

keywords banachballcombinationsconvexdiametereveryopenslices

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original abstract

We show that every Banach space containing isomorphic copies of $c_0$ can be equivalently renormed so that every nonempty relatively weakly open subset of its unit ball has diameter 2 and, however, its unit ball still contains convex combinations of slices with diameter arbitrarily small, which improves in a optimal way the known results about the size of this kind of subsets in Banach spaces.

Extreme differences between weakly open subsets and convex combinations of slices in Banach spaces

discussion (0)