Self Jung constants and product spaces (Q2725639)

The (finite) self-Jung constant of a Banach space may be defined as the smallest number \(r\) for which every (finite-dimensional) closed convex set with diameter less than 2 is contained in a ball, with centre in the set and radius \(r\). The authors estimate these constants for the direct sum of two Banach spaces, in terms of the corresponding constants of the component subspaces; it is assumed that the norm on the direct sum is induced by an absolute norm on \({\mathbb R}^2\). It is known that \(B\)-convexity of a Banach space is a consequence of its finite self-Jung constant being less than 2; a new proof thereof is given here.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00019].