Performance of the Thresholding Greedy Algorithm with larger greedy sums

The goal of this paper is to study the performance of the Thresholding Greedy Algorithm (TGA) when we increase the size of greedy sums by a constant factor λ⩾1. We introduce the so-called λ-almost greedy and λ-partially greedy bases. The case when λ=1 gives us the classical definitions of almost gre...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 525; no. 1; p. 127126
Main Author: Chu, Hùng Việt
Format: Journal Article
Language:English
Published: Elsevier Inc 01.09.2023
Subjects:
Almost greedy
Characterizations
Greedy
Partially greedy
Reverse partially greedy bases
Reverse partially greedy bases
Characterizations
Partially greedy
Greedy
Almost greedy
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:The goal of this paper is to study the performance of the Thresholding Greedy Algorithm (TGA) when we increase the size of greedy sums by a constant factor λ⩾1. We introduce the so-called λ-almost greedy and λ-partially greedy bases. The case when λ=1 gives us the classical definitions of almost greedy and (strong) partially greedy bases. We show that a basis is almost greedy if and only if it is λ-almost greedy for all (some) λ⩾1. However, for each λ>1, there exists an unconditional basis that is λ-partially greedy but is not 1-partially greedy. Furthermore, we investigate and give examples when a basis is(1)not almost greedy with constant 1 but is λ-almost greedy with constant 1 for some λ>1, and(2)not strong partially greedy with constant 1 but is λ-partially greedy with constant 1 for some λ>1. Finally, we prove various characterizations of different greedy-type bases.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127126