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Search name	Searched On	Run search
[in Journal: Journal of Topology and Analysis] AND [Keyword: Reflexivity] (1)	29 Mar 2025	Run
[in Journal: Journal of Enterprising Culture] AND [Keyword: Reflexivity] (1)	29 Mar 2025	Run
[in Journal: International Journal of Biomathematics] AND [Keyword: Equilibrium] (13)	29 Mar 2025	Run
[in Journal: Biomedical Engineering: Applications, Basis and Communications] AND [K... (1)	29 Mar 2025	Run
[in Journal: Surface Review and Letters] AND [Keyword: Reflectance] (2)	29 Mar 2025	Run

articleNo Access
On metric characterizations of the Radon–Nikodým and related properties of Banach spaces
- Mikhail I. Ostrovskii
Journal of Topology and Analysis16 Jun 2014
Preview Abstract
We find a class of metric structures which do not admit bilipschitz embeddings into Banach spaces with the Radon–Nikodým 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.

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