On Klee's Convex Body Problem and Application 程立新 (厦门大学) In 1959, Klee asked that for what Banach spaces the following hold. 1. Every convex body can be uniformly approximated by strictly convex bodies; 2. Every convex body can be uniformly approximated by (Gâteaux) smooth convex bodies; 3. Every convex body can be uniformly approximated by strictly convex and smooth convex bodies. This talk is divided into two parts. The first part is dedicated to solving Klee’s problem. The second one is to use the results we have obtained and some stronger versions to characterize some geometric and topological properties of Banach spaces. (This is a joint work with Prof. Chunlan Jiang, Prof. Liping Yuan and Prof. Wuyi He.) |
