Metric embeddings of Laakso graphs into Banach spaces

被引：1
|
作者：
Dilworth, S. J. [1 ,2 ]
Kutzarova, Denka [1 ,2 ,3 ]
Stankov, Svetozar [4 ]
机构：
[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA
[2] Bulgarian Acad Sci, Inst Math, Sofia, Bulgaria
[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA
[4] Bulgarian Acad Sci, Dept Math, Sofia, Bulgaria
来源：
BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2022年 / 16卷 / 04期
关键词：
Laakso graph; Bilipschitz embeddings; Super-reflexivity; Banach spaces; REFLEXIVITY; GIRTH;
D O I：
10.1007/s43037-022-00212-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let X be Banach space which is not super-reflexive. Then, for each n >= 1 and epsilon > 0, we exhibit metric embeddings of the Laakso graph L-n into X with distortion less than 2 + epsilon and into L-1[0, 1] with distortion 4/3. The distortion of an embedding of L-2 (respectively, the diamond graph D-2) into L-1 [0, 1] is at least 9/8 (respectively, 5/4).
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页数：14
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