| Résume | The notion of stable norm was introduced by Krivine and Maurey in the early 80's in order to study the subspace structure of Banach spaces. The connection with nonlinear (uniform) embeddings was further studied by Raynaud. In the mid 2000's Kalton proved that every stable metric space admits a uniform and coarse embedding into a reflexive space, and he asked whether every reflexive space admits a coarse or a uniform embedding into a stable space. This problem is still open. In this talk we will discuss the relationship between two metric invariants, namely, Kalton's property Q and upper-stability (a natural relaxation of stability), and their connection with Kalton's problem. This is joint work in progress with Th. Schlumprecht (Texas A&M) and A. Zsák (Peterhouse, Cambridge). |
