Metric embeddings of Laakso graphs into Banach spaces

2022/03/15 by S. J. Dilworth, Dilworth, S. J., Denka Kutzarova +3
Medicine · #46B85 (Primary) 46B20 (Secondary) #Chronic Myeloid Leukemia Treatments #FOS: Mathematics #Functional Analysis (math.FA) #IgG4-Related and Inflammatory Diseases

paper · pdf · doi:10.48550/arxiv.2203.08229

openalex publication_date 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be Banach space which is not super-reflexive. Then, for each n≥1 and ε>0, we exhibit metric embeddings of the Laakso graph L_n into X with distortion less than 2+ε and into L₁[0,1] with distortion 4/3. The distortion of an embedding of L₂ (respectively, the diamond graph D₂) into L₁[0,1] is at least 9/8 (respectively, 5/4).

Related

• Linear properties of Banach spaces and low distortion embeddings of metric graphs
• Asymptotic and nonlinear geometries of Banach spaces and their interactions
• Some comments on Laakso graphs and sets of differences
• Low distortion embeddings into Asplund Banach spaces
• Graph embeddings into Hamming spaces