Zimní škola

On maximal symmetry in Banach spaces and isometric representations of Polish groups.

It follows from the theory of Lipschitz free Banach spaces that any Polish group is topologically isomorphic to an index 2 closed subgroup of the isometry group of a separable Banach space. However, this result gives almost no information about the relation between the isomorphic structure of the group and the Banach space. As a reversal, we study which groups can appear as the isometry group of a fixed separable Banach space under equivalent renormings. In particular, we answer a longstanding problem of G. Wood on whether GL(X) always contains a maximal bounded subgroup. This is joint work with V. Ferenczi.