{"title":"On some characterizations of greedy-type bases","authors":"Pablo M. Berná , Hùng Việt Chu","doi":"10.1016/j.exmath.2022.06.003","DOIUrl":null,"url":null,"abstract":"<div><p><span>In 1999, S. V. Konyagin and V. N. Temlyakov introduced the so-called Thresholding </span>Greedy Algorithm<span>. Since then, there have been many interesting and useful characterizations of greedy-type bases in Banach spaces. In this article, we study and extend several characterizations of greedy and almost greedy bases in the literature. Along the way, we give various examples to complement our main results. Furthermore, we propose a new version of the so-called Weak Thresholding Greedy Algorithm (WTGA) and show that the convergence of this new algorithm is equivalent to the convergence of the WTGA.</span></p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"40 4","pages":"Pages 1135-1158"},"PeriodicalIF":0.8000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086922000482","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
In 1999, S. V. Konyagin and V. N. Temlyakov introduced the so-called Thresholding Greedy Algorithm. Since then, there have been many interesting and useful characterizations of greedy-type bases in Banach spaces. In this article, we study and extend several characterizations of greedy and almost greedy bases in the literature. Along the way, we give various examples to complement our main results. Furthermore, we propose a new version of the so-called Weak Thresholding Greedy Algorithm (WTGA) and show that the convergence of this new algorithm is equivalent to the convergence of the WTGA.
1999年，S. V. Konyagin和V. N. Temlyakov引入了所谓的阈值贪婪算法。此后，对Banach空间中的贪心型基有了许多有趣而有用的刻画。本文研究并推广了文献中关于贪心基和几乎贪心基的几个刻画。在此过程中，我们给出了各种例子来补充我们的主要结果。在此基础上，提出了一种新的弱阈值贪婪算法(WTGA)，并证明了该算法的收敛性等同于WTGA算法的收敛性。
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