On Weighted Greedy-Type Bases

We study weights for the thresholding greedy algorithm, aiming to extend previous work on sequential weights ς on N to weights ω on P ( N ) . We revisit major results on weighted greedy-type bases in this new setting including characterizations of ω -(almost) greedy bases and the equivalence between...

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Bibliographic Details
Published in:Boletim da Sociedade Brasileira de Matemática Vol. 54; no. 4; p. 49
Main Author: Chu, Hùng Việt
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2023
Springer Nature B.V
Subjects:
Approximation
Greedy algorithms
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Semi-greedy
46B15
Almost greedy
41A65
Thresholding greedy algorithm
Partially greedy
Greedy
Weight
ISSN:1678-7544, 1678-7714
Online Access:Get full text
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Summary:We study weights for the thresholding greedy algorithm, aiming to extend previous work on sequential weights ς on N to weights ω on P ( N ) . We revisit major results on weighted greedy-type bases in this new setting including characterizations of ω -(almost) greedy bases and the equivalence between ω -semi-greedy bases and ω -almost greedy bases. Some new results are encountered along the way. For example, we show that there exists an ω -greedy unconditional basis that is not ς -almost greedy for any weight sequence ς . Moreover, a basis is unconditional if and only if it is ω -greedy for some weight ω . Similarly, a basis is quasi-greedy if and only if it is ω -almost greedy for some weight ω .
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ISSN:1678-7544
1678-7714
DOI:10.1007/s00574-023-00367-3