Nonlinear aspects of super weakly compact sets
Abstract
The notion of super weak compactness for subsets of Banach spaces is a strengthening of the weak compactness that can be described as a local version of super-reflexivity. A recent result of K. Tu which establishes that the closed convex hull of a super weakly compact set is super weakly compact has removed the main obstacle to further development of the theory. In this paper we provide a variety of results around super weak compactness in order to show the great scope of this notion. We also give non linear characterizations of super weak compactness in terms of the (non) embeddability of special trees and graphs. We conclude with a few relevant examples of super weakly compact sets in non super-reflexive Banach spaces.
Cite
@article{arxiv.2003.01030,
title = {Nonlinear aspects of super weakly compact sets},
author = {Gilles Lancien and Matias Raja},
journal= {arXiv preprint arXiv:2003.01030},
year = {2021}
}
Comments
19 pages. This is the second arXiv version of this paper. The proof of Theorem 2.2 contained a mistake in the first version. We now refer to a paper by Kun Tu instead. The rest our paper is essentially unchanged. This paper has been accepted fro publication in the "Annales de l'Institut Fourier"