The Mazur property for compact sets
The author establishes the following smoothness property. Let X be a Banach space. Every compact convex set of X is the intersection of balls containing it if and only if the cone of the extreme points of the dual X' is dense in X' with respect to the topology of uniform convergence on compact sets of X. This characterization is also used to derive other results and applications as stability under \(c_ 0\) and \(\ell_ p\) sums, \(1\leq p<\infty\), and renorming theorems. Some of the author's proofs unify and simplify previous proof techniques.
topology of uniform convergence on compact sets
stability under \(c_ 0\) and \(\ell _ p\) sums
scientific article; zbMATH DE number 4065670