Wide and tight spherical hulls of bounded sets in Banach spaces

Abstract

Let $A$ be a bounded closed convex set in a Banach space. The boundaries of the wide spherical hull $\eta \left(A\right)$ and the tight spherical hull $\theta \left(A\right)$ are characterized, the existence of diametral points of these three sets are discussed, and a further relation between these three sets is clarified. Moreover, a new characterization of balls is presented.