On metric characterizations of some classes of Banach spaces (Q2844651)
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scientific article; zbMATH DE number 6981801
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On metric characterizations of some classes of Banach spaces |
scientific article; zbMATH DE number 6981801 |
Statements
29 August 2013
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20 November 2018
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Banach space
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diamond graphs
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expander graphs
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Laakso graphs
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Lipschitz embedding
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Radon-Nikodým property
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bi-Lipschitz embedding
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Heisenberg group
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Markov convexity
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superreflexive Banach space
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thick family of geodesics
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On metric characterizations of some classes of Banach spaces (English)
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The paper under review can be divided into two parts. The first part deals with the metric characterizations of Banach spaces with no cotype and no type \( > 1 \) in terms of graphs with uniformly bounded degrees. It is proved in the second part that Banach spaces containing bilipschitz images of the infinite diamond do not possess the Radon-Nikodým property. At the end of the paper, the author gives a new proof of the Cheeger-Kleiner result (see Corollary 1.7 from \textit{J. Cheeger} and \textit{B. Kleiner} [Geom. Funct. Anal. 19, No. 4, 1017--1028 (2009; Zbl 1200.58007)] on Banach spaces containing bilipschitz images of the Laakso space.
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