17:00
The classical Banach-Stone theorem describes the structure of onto linear isometries of the Banach space $C(K)$ of all continuous functions on a compact Hausdorff space $K$. Namely, such an isometry is always a product of a composition operator with a homeomorphism symbol and a multiplication operator with a continuous symbol which has modulus 1.
Recently, similar results have been obtained in the setting of certain class of probability measures. In my talk first, I will give an overview of these results, and then I will present the main ideas of a recent work. Namely, I will provide a characterisation of all surjective isometries of the (non-linear) space of all Borel probability measures on an arbitrary separable Banach space with respect to the famous Levy-Prokhorov distance (which metrises the weak convergence). This is a recent joint work with Tamas Titkos (MTA Alfred Renyi Institute of Mathematics, Budapest, Hungary).