Big Weak Open Radius Versus Big Slice Diameter
Abstract
Abstract We show that there exists a Banach space in which every non-empty weakly open subset of its unit ball has radius one, the maximum possible value, but the infimum of the diameter of its slices is exactly one, so extremely far from its maximum. In fact, we show that there is a wide class of non-isomorphic Banach spaces satisfying this extreme difference between the behaviour of the radius and the diameter of non-empty weakly open subsets.
Fields of Study & Subjects
Advanced Banach Space Theory
Advanced Topology and Set Theory
Fuzzy and Soft Set Theory
Publication details
- Journal / source
- Mediterranean Journal of Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 23
- Issue
- 4
- Publication date
- 1 June 2026
- Language
- EN