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).

引用

页数：14

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