On the geometry of the countably branching diamond graphs

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the geometry of the countably branching diamond graphs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the geometry of the countably branching diamond graphs

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

JOURNAL OF FUNCTIONAL ANALYSIS

ISSN

0022-1236

e-ISSN

1096-0783

Svazek periodika

273

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

50

Strana od-do

3150-3199

Kód UT WoS článku

000412150600004

EID výsledku v databázi Scopus

2-s2.0-85021173571