More on the (uniform) Mazur intersection property
Volume 278 / 2024
Studia Mathematica 278 (2024), 49-67
MSC: Primary 46B20
DOI: 10.4064/sm231207-19-4
Published online: 3 October 2024
Abstract
We introduce two moduli of $w^*$-semidenting points and characterise the Mazur Intersection Property (MIP) and the Uniform Mazur Intersection Property (UMIP) in terms of these moduli.
We show that a property slightly stronger than UMIP already implies uniform convexity of the dual. This may lead to a possible approach towards the long standing open question whether UMIP implies the existence of an equivalent uniformly convex renorming.
We also obtain a condition for stability of UMIP under $\ell_p$-sums.
