Metric embeddings of Laakso graphs into Banach spaces

S. J. Dilworth, Denka Kutzarova, Svetozar Stankov

Research output: Contribution to journalArticlepeer-review

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 Ln 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).

Original languageEnglish (US)
Article number60
JournalBanach Journal of Mathematical Analysis
Volume16
Issue number4
DOIs
StatePublished - Oct 2022

Keywords

  • Banach spaces
  • Bilipschitz embeddings
  • Laakso graph
  • Super-reflexivity

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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