On the geometry of the countably branching diamond graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00314831" target="_blank" >RIV/68407700:21230/17:00314831 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jfa.2017.05.013" target="_blank" >http://dx.doi.org/10.1016/j.jfa.2017.05.013</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2017.05.013" target="_blank" >10.1016/j.jfa.2017.05.013</a>
Alternative languages
Result language
angličtina
Original language name
On the geometry of the countably branching diamond graphs
Original language description
In this article, the bi-Lipschitz embeddability of the sequence of countably branching diamond graphs (D-k(omega))k is an element of N is investigated. In particular it is shown that for every epsilon > 0 and k is an element of N, D-k(omega) embeds bi-Lipschiztly with distortion at most 6(1+epsilon) 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 (D-k(omega))k is an element of N 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 L-p-spaces and to some problems in renorming theory are also discussed. (C) 2017 Elsevier Inc. All rights reserved.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
JOURNAL OF FUNCTIONAL ANALYSIS
ISSN
0022-1236
e-ISSN
1096-0783
Volume of the periodical
273
Issue of the periodical within the volume
10
Country of publishing house
US - UNITED STATES
Number of pages
50
Pages from-to
3150-3199
UT code for WoS article
000412150600004
EID of the result in the Scopus database
2-s2.0-85021173571