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 language | English (US) |
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Article number | 60 |
Journal | Banach Journal of Mathematical Analysis |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - Oct 2022 |
Keywords
- Banach spaces
- Bilipschitz embeddings
- Laakso graph
- Super-reflexivity
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory