This is an announcement for the paper "On metric characterizations of the Radon-Nikodym and related properties of Banach spaces" by Mikhail I. Ostrovskii.
Abstract: We find a class of metric structures which do not admit bilipschitz embeddings into Banach spaces with the Radon-Nikod'ym property. Our proof relies on Chatterji's (1968) martingale characterization of the RNP and does not use the Cheeger's (1999) metric differentiation theory. The class includes the infinite diamond and both Laakso (2000) spaces. We also show that for each of these structures there is a non-RNP Banach space which does not admit its bilipschitz embedding. We prove that a dual Banach space does not have the RNP if and only if it admits a bilipschitz embedding of the infinite diamond. The paper also contains related characterizations of reflexivity and the infinite tree property.
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary: 46B22, Secondary: 05C12, 30L05, 46B10, 46B85, 54E35
Submitted from: ostrovsm@stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1302.5968
or