Extreme differences between weakly open subsets and convex combinations of slices in Banach spaces
Functional Analysis
2014-10-17 v3
Abstract
We show that every Banach space containing isomorphic copies of 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.
Keywords
Cite
@article{arxiv.1309.4950,
title = {Extreme differences between weakly open subsets and convex combinations of slices in Banach spaces},
author = {Julio Becerra Guerrero and Ginés López-Pérez and Abraham Rueda Zoca},
journal= {arXiv preprint arXiv:1309.4950},
year = {2014}
}
Comments
arXiv admin note: text overlap with arXiv:1304.4397