Approximation properties, decompositions and bases of free spaces
Abstract:
For a metric space $M$ equipped with a distinguished element $0$, the Lipschitz-free space $cal F (M)$ is the canonical predual of the space of all real-valued Lipschitz functions on $M$ vanishing at $0$. We will discuss approximation properties and the existence of finite dimensional-decompositions or Schauder bases of Lipschitz-free spaces. We will present recent results saying that $cal F (M)$, where $M$ is a doubling metric space, has the bounded approximation property and that $cal F (ell_1^N)$ and $cal F (ell_1)$ have a Schauder basis. The talk will be based on a joint work with G. Lancien and P. Hajek.
CZ
