Embeddability of locally finite metric spaces into Banach spaces is finitely determined

DOI10.1090/S0002-9939-2011-11272-3zbMath1276.46013arXiv1103.0748OpenAlexW2096848739MaRDI QIDQ2845546

Mikhail I. Ostrovskii

Publication date: 2 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.0748

zbMATH Keywords

Banach spacecoarse embeddingbilipschitz embeddinglocally finite metric space

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Ultraproduct techniques in Banach space theory (46B08) Distance in graphs (05C12) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

Related Items (16)

Metric Characterizations of Some Classes of Banach Spaces ⋮ Vertical perimeter versus horizontal perimeter ⋮ Barycentric gluing and geometry of stable metrics ⋮ DISTORTION IN THE FINITE DETERMINATION RESULT FOR EMBEDDINGS OF LOCALLY FINITE METRIC SPACES INTO BANACH SPACES ⋮ Distortion in the metric characterization of superreflexivity in terms of the infinite binary tree ⋮ On embeddings of locally finite metric spaces into \(\ell_p\) ⋮ Metric characterizations of superreflexivity in terms of word hyperbolic groups and finite graphs ⋮ The non-linear geometry of Banach spaces after Nigel Kalton ⋮ Quantitative nonlinear embeddings into Lebesgue sequence spaces ⋮ (β)-distortion of some infinite graphs ⋮ Generalized transportation cost spaces ⋮ Book Review: Metric embeddings: bilipschitz and coarse embedddings into Banach spaces ⋮ A characterization of superreflexivity through embeddings of lamplighter groups ⋮ Thick families of geodesics and differentiation ⋮ Group approximation in Cayley topology and coarse geometry. II: Fibred coarse embeddings ⋮ Tight Embeddability of Proper and Stable Metric Spaces

Cites Work

• Metrical characterization of super-reflexivity and linear type of Banach spaces
• The Unconditional Basic Sequence Problem
• Coarse embeddability into Banach spaces
• Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
• Uniform embeddings of bounded geometry spaces into reflexive Banach space
• Application des ultraproduits à l'étude des espaces et des algèbres de Banach
• Embeddings of locally finite metric spaces into Banach spaces
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