Connections Between Metric Characterizations of Superreflexivity and the Radon-Nikodý Property for Dual Banach Spaces

Canadian mathematical bulletin

Mikhail I. Ostrovskii¹ 

[1] Department of Mathematics and Computer Science, St. John's University, 8000 Utopia Parkway, Queens, NY 11439, USA

关键词: Banach space;    diamond graph;    finite representability;    metric characterization;    Radon-Nikodým property;    superreflexivity;   

DOI  :  10.4153/CMB-2014-049-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Johnson and Schechtman (2009)characterized superreflexivity in terms of finite diamond graphs.The present author characterized the Radon-Nikodým property(RNP) for dual spaces in terms of the infinite diamond. Thispaperis devoted to further study of relations between metriccharacterizations of superreflexivity and the RNP for dual spaces.The main result is that finite subsets of any set $M$ whoseembeddability characterizes the RNP for dual spaces, characterizesuperreflexivity. It is also observed that the converse statementdoes not hold, and that $M=ell_2$ is a counterexample.

【 授权许可】

Unknown