Linear properties of Banach spaces and low distortion embeddings of metric graphs

2016/03/02 by Prochazka, Antonin
#46B20 #46B85 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1603.00741

Abstract

We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for ℓ₁ⁿ being (1+ε)-isomorphic to a subspace of a Banach space X.

Related

• Metric embeddings of Laakso graphs into Banach spaces
• Low distortion embeddings into Asplund Banach spaces
• Remarks on quasi-isometric non-embeddability into uniformly convex Banach spaces
• Asymptotic and nonlinear geometries of Banach spaces and their interactions
• Sparsity and non-Euclidean embeddings