The generalised (uniform) Mazur Intersection Property

Article Type

Research Article

Publication Title

Journal of Mathematical Analysis and Applications

Abstract

Given a family C of closed bounded convex sets in a Banach space X, we say that X has the C-MIP if every C∈C is the intersection of closed balls containing it. In this paper, we introduce a stronger version of C-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) C-MIP and characterise them analogously. Even in this case, the strong C-UMIP appears to have richer characterisations than the C-UMIP.

DOI

https://10.1016/j.jmaa.2023.127001

Publication Date

7-1-2023

Comments

Open Access, Green

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