Thu, Apr 10
1:00 PM — 2:00 AM
NAC160 Convent Avenue
Mikhail I. Ostrovskii (St. John's University),Metric characterization of the Radon-Nikodym property in Banach spaces
The Radon-Nikod'ym property (RNP) is one of the most basic and important isomorphic invariants of Banach spaces. A Banach space X is said to have the Radon-Nikodym property if an analogue of the Radon-Nikodym theorem holds for X-valued measures which are absolutely continuous with respect to some real-valued measures. This property can be characterized in many different analytic, geometric, and probabilistic ways. Possibly the most well-known is the characterization in terms of Lipschitz functions (goes back to Clarkson (1936) and Gelfand (1938)): A Banach space X has the RNP if and only if each X-valued Lipschitz function on the real line is almost everywhere differentiable. The RNP plays an important role in the theory of metric embeddings (works of Cheeger, Kleiner, Lee, and Naor (2006--2009)). In this connection Johnson (2009) suggested the problem of metric characterization of RNP. The goal of the talk is to present a solution of this problem in terms of thick families of geodesics.