Tree metrics and their Lipschitz-free spaces

DOI10.1090/S0002-9939-2010-10421-5zbMath1222.46010arXiv0904.3178OpenAlexW2963642874MaRDI QIDQ3065710

Alexandre Godard

Publication date: 6 January 2011

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

Full work available at URL: https://arxiv.org/abs/0904.3178

zbMATH Keywords

Lipschitz-free spacesmetric treesfour-point propertysubspaces of \(L_{1}\)

Mathematics Subject Classification ID

Trees (05C05) Metric spaces, metrizability (54E35) Classical Banach spaces in the general theory (46B25) Isometric theory of Banach spaces (46B04)

Related Items (41)

Lipschitz-free spaces and Schur properties ⋮ Lipschitz-free spaces over ultrametric spaces ⋮ Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions ⋮ Kantorovich distance on finite metric spaces: Arens-Eells norm and CUT norms ⋮ On the unique predual problem for Lipschitz spaces ⋮ A characterisation of octahedrality in Lipschitz-free spaces ⋮ Absolute Lipschitz extendability and linear projection constants ⋮ Cantor sets of low density and Lipschitz functions on \(C^1\) curves ⋮ Approximation properties and Schauder decompositions in Lipschitz-free spaces ⋮ On projectional skeletons and the Plichko property in Lipschitz-free Banach spaces ⋮ Complementability of isometric copies of \(\ell_1\) in transportation cost spaces ⋮ Lipschitz functions on unions and quotients of metric spaces ⋮ Some remarks on Schauder bases in Lipschitz free spaces ⋮ Wasserstein distance and metric trees ⋮ Lipschitz-free Spaces on Finite Metric Spaces ⋮ Lipschitz functions on quasiconformal trees ⋮ ISOMETRIC REPRESENTATION OF LIPSCHITZ‐FREE SPACES OVER CONVEX DOMAINS IN FINITE‐DIMENSIONAL SPACES ⋮ Injectivity of Lipschitz operators ⋮ On relations between transportation cost spaces and \(\ell_1\) ⋮ Geometry and volume product of finite dimensional Lipschitz-free spaces ⋮ Lipschitz free \(p\)-spaces for \(0 < p < 1\) ⋮ Embeddings of Lipschitz-free spaces into \(\ell_1\) ⋮ The non-linear geometry of Banach spaces after Nigel Kalton ⋮ On Schauder bases in Lipschitz-free spaces ⋮ Free spaces over some proper metric spaces ⋮ The metric approximation property and Lipschitz-free spaces over subsets of \(\mathbb{R}^N\) ⋮ Free Banach spaces and the approximation properties ⋮ Unconditional almost squareness and applications to spaces of Lipschitz functions ⋮ Embeddability of \(\ell_p\) and bases in Lipschitz free \(p\)-spaces for \(0 < p \leq 1\) ⋮ Examples and applications of the density of strongly norm attaining Lipschitz maps ⋮ On the dynamics of Lipschitz operators ⋮ Generalized transportation cost spaces ⋮ On the structure of Lipschitz-free spaces ⋮ Analysis on Laakso graphs with application to the structure of transportation cost spaces ⋮ Lipschitz free spaces over locally compact metric spaces ⋮ Lipschitz \(p\)-compact mappings ⋮ On strongly norm attaining Lipschitz maps ⋮ Isomorphisms between spaces of Lipschitz functions ⋮ Isometric structure of transportation cost spaces on finite metric spaces ⋮ Products of Lipschitz-free spaces and applications ⋮ Asymmetric free spaces and canonical asymmetrizations

Cites Work

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• A note on the metric properties of trees
• Spaces of Lipschitz and Hölder functions and their applications
• \(\Lambda\)-manifolds
• The Lipschitz free Banach spaces of $C(K)$-spaces
• Planar Earthmover Is Not in $L_1$
• Lipschitz-free Banach spaces

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