Renorming spaces with greedy bases

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Renorming spaces with greedy bases
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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