On some characterizations of greedy-type bases

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2022Embargo end date: 01 Jan 2022 English Publisher:Elsevier BVJournal:Expositiones Mathematicae, volume 40, pages 1,135-1,158 (issn: 0723-0869,

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Authors: Pablo M. Berná; Hùng Việt Chu;

doi: 10.1016/j.exmath.2022.06.003 , 10.48550/arxiv.2201.12029

arXiv: 2201.12029

On some characterizations of greedy-type bases

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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.

Keywords

Mathematics - Functional Analysis, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), almost greedy bases, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, greedy bases, thresholding greedy algorithm, Functional Analysis (math.FA)

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