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
Recommended Citation
Bandyopadhyay, Pradipta and Gothwal, Deepak, "The generalised (uniform) Mazur Intersection Property" (2023). Journal Articles. 3670.
https://digitalcommons.isical.ac.in/journal-articles/3670
Comments
Open Access, Green