English

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 c0c_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.

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