On some characterizations of greedy-type bases

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 gre...

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Bibliographic Details
Published in:Expositiones mathematicae Vol. 40; no. 4; pp. 1135 - 1158
Main Authors: Berná, Pablo M., Chu, Hùng Việt
Format: Journal Article
Language:English
Published: Elsevier GmbH 01.12.2022
Subjects:
Almost greedy bases
Greedy bases
Thresholding greedy algorithm
secondary
Greedy bases
Thresholding greedy algorithm
Almost greedy bases
primary
ISSN:0723-0869, 1878-0792
Online Access:Get full text
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Summary: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.
ISSN:0723-0869
1878-0792
DOI:10.1016/j.exmath.2022.06.003