کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772320 | 1413360 | 2017 | 50 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the geometry of the countably branching diamond graphs
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
In this article, the bi-Lipschitz embeddability of the sequence of countably branching diamond graphs (DkÏ)kâN is investigated. In particular it is shown that for every ε>0 and kâN, DkÏ embeds bi-Lipschiztly with distortion at most 6(1+ε) into any reflexive Banach space with an unconditional asymptotic structure that does not admit an equivalent asymptotically uniformly convex norm. On the other hand it is shown that the sequence (DkÏ)kâN does not admit an equi-bi-Lipschitz embedding into any Banach space that has an equivalent asymptotically midpoint uniformly convex norm. Combining these two results one obtains a metric characterization in terms of graph preclusion of the class of asymptotically uniformly convexifiable spaces, within the class of reflexive Banach spaces with an unconditional asymptotic structure. Applications to bi-Lipschitz embeddability into Lp-spaces and to some problems in renorming theory are also discussed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 273, Issue 10, 15 November 2017, Pages 3150-3199
Journal: Journal of Functional Analysis - Volume 273, Issue 10, 15 November 2017, Pages 3150-3199
نویسندگان
Florent Baudier, Ryan Causey, Stephen Dilworth, Denka Kutzarova, Nirina L. Randrianarivony, Thomas Schlumprecht, Sheng Zhang,