Ball separation characterization of ball dentability and related properties

TL;DR

This paper investigates how the concept of ball separation applies to Banach spaces with dentable unit balls, extending classical Euclidean separation properties to a broader functional analysis context.

Contribution

It introduces a ball separation characterization for Banach spaces with dentable unit balls and explores related geometric properties.

Findings

Established a new separation characterization in dentable Banach spaces

Connected separation properties with dentability of the unit ball

Extended Euclidean separation concepts to infinite-dimensional spaces

Abstract

In Euclidean spaces, every closed, bounded, convex set can be characterized by two equivalent notions of separation properties. This is not true in general for arbitrary Banach spaces. In this work, we present a ball separation characterization for spaces where the unit ball is dentable. We also explore related properties.