The Generalised (Uniform) Mazur Intersection Property
Functional Analysis
2023-01-06 v1
Abstract
Given a family of closed bounded convex sets in a Banach space , we say that has the -MIP if every is the intersection of the closed balls containing it. In this paper, we introduce a stronger version of the -MIP and show that it is a more satisfactory generalisation of the MIP inasmuch as one can obtain complete analogues of various characterisations of the MIP. We also introduce uniform versions of the (strong) -MIP and characterise them analogously. Even in this case, the strong -UMIP appears to have richer characterisations than the -UMIP.
Keywords
Cite
@article{arxiv.2301.01974,
title = {The Generalised (Uniform) Mazur Intersection Property},
author = {Pradipta Bandyopadhyay and Deepak Gothwal},
journal= {arXiv preprint arXiv:2301.01974},
year = {2023}
}