Renorming spaces with greedy bases

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F14%3A00309450" target="_blank" >RIV/68407700:21230/14:00309450 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jat.2014.09.001" target="_blank" >http://dx.doi.org/10.1016/j.jat.2014.09.001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jat.2014.09.001" target="_blank" >10.1016/j.jat.2014.09.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Renorming spaces with greedy bases

Popis výsledku v původním jazyce

We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given epsilon > 0, so that the basis becomes (1+epsilon)-democratic, and hence (2+epsilon)-greedy, with respect to the new norm. If in addition the basis is bidemocratic, then there is a renorming so that in the new norm the basis is (1+ epsilon)greedy. We also prove that in the latter result the additional assumption of the basis being bidemocratic can be removed for a large class of bases. Applications include the Haar systems in L-p [0, 1], 1 < p < infinity), and in dyadic Hardy space H-1, as well as the unit vector basis of Tsirelson space. (C) 2014 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Renorming spaces with greedy bases

Popis výsledku anglicky

We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given epsilon > 0, so that the basis becomes (1+epsilon)-democratic, and hence (2+epsilon)-greedy, with respect to the new norm. If in addition the basis is bidemocratic, then there is a renorming so that in the new norm the basis is (1+ epsilon)greedy. We also prove that in the latter result the additional assumption of the basis being bidemocratic can be removed for a large class of bases. Applications include the Haar systems in L-p [0, 1], 1 < p < infinity), and in dyadic Hardy space H-1, as well as the unit vector basis of Tsirelson space. (C) 2014 Elsevier Inc. All rights reserved.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Journal of Approximation Theory

ISSN

0021-9045

e-ISSN

—

Svazek periodika

188

Číslo periodika v rámci svazku

DEC

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

18

Strana od-do

39-56

Kód UT WoS článku

000345186000003

EID výsledku v databázi Scopus

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