Yet another short proof of Bourgain's distortion estimate for embedding of trees into uniformly convex Banach spaces

DOI10.1007/s11856-014-0024-4zbMath1314.46028OpenAlexW2079619631MaRDI QIDQ2017169

Benoît R. Kloeckner

Publication date: 25 June 2014

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-014-0024-4

zbMATH Keywords

treeuniformly convex Banach spacebi-Lipschitz embedding

Mathematics Subject Classification ID

Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

Related Items (13)

Power type asymptotically uniformly smooth and asymptotically uniformly flat norms ⋮ Metric Characterizations of Some Classes of Banach Spaces ⋮ Nonlinear aspects of super weakly compact sets ⋮ Old and new challenges in Hadamard spaces ⋮ Distortion of embeddings of binary trees into diamond graphs ⋮ \(\xi\)-asymptotically uniformly smooth, \(\xi\)-asymptotically uniformly convex, and (\(\beta\)) operators ⋮ Metric characterizations of superreflexivity in terms of word hyperbolic groups and finite graphs ⋮ Power type \(\xi\)-asymptotically uniformly smooth and \(\xi\)-asymptotically uniformly flat norms ⋮ A new approach to low-distortion embeddings of finite metric spaces into non-superreflexive Banach spaces ⋮ (β)-distortion of some infinite graphs ⋮ No dimension reduction for doubling subsets of \(\ell_q\) when \(q>2\) revisited ⋮ On the embeddability of the family of countably branching trees into quasi-reflexive Banach spaces ⋮ A characterization of superreflexivity through embeddings of lamplighter groups

Cites Work

• The metrical interpretation of superreflexivity in Banach spaces
• Sharp uniform convexity and smoothness inequalities for trace norms
• The Euclidean distortion of complete binary trees
• Markov convexity and local rigidity of distorted metrics
• On embedding trees into uniformly convex Banach spaces
• Metric Characterizations of Some Classes of Banach Spaces
• DIAMOND GRAPHS AND SUPER-REFLEXIVITY
• Trees and Markov convexity

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