A duality operators/Banach spaces
Abstract
Given a set of operators between subspaces of spaces, we characterize the operators between subspaces of spaces that remain bounded on the -valued space for every Banach space on which elements of the original class are bounded. This is a form of the bipolar theorem for a duality between the class of Banach spaces and the class of operators between subspaces of spaces, essentially introduced by Pisier. The methods we introduce allow us to recover also the other direction --characterizing the bipolar of a set of Banach spaces--, which had been obtained by Hernandez in 1983.
Cite
@article{arxiv.2101.07666,
title = {A duality operators/Banach spaces},
author = {Mikael de la Salle},
journal= {arXiv preprint arXiv:2101.07666},
year = {2021}
}
Comments
34 pages. Old project, already announced at several occasions in 2016, and that took a long time to be completed. Comments welcome v2: 37 pages. Section 5 added on the duality between Banach spaces and operators on full Lp spaces. A few references added