Weak weight-semi-greedy Markushevich bases

The main purpose of this paper is to study weight-semi-greedy Markushevich bases, and in particular, find conditions under which such bases are weight-almost greedy. In this context, we prove that, for a large class of weights, the two notions are equivalent. We also show that all weight semi-greedy...

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Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Jg. 154; H. 4; S. 1118 - 1179
Hauptverfasser: Berasategui, Miguel, Lassalle, Silvia
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Edinburgh, UK Royal Society of Edinburgh Scotland Foundation 01.08.2024
Cambridge University Press
Schlagworte:
Algorithms
Approximation
Banach spaces
Chebyshev approximation
Context
Greedy algorithms
bases
46B20
46B15
greedy approximation
weights
41A65
ISSN:0308-2105, 1473-7124
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Zusammenfassung:The main purpose of this paper is to study weight-semi-greedy Markushevich bases, and in particular, find conditions under which such bases are weight-almost greedy. In this context, we prove that, for a large class of weights, the two notions are equivalent. We also show that all weight semi-greedy bases are truncation quasi-greedy and weight-superdemocratic. In all of the above cases, we also bring to the context of weights the weak greedy and Chebyshev greedy algorithms—which are frequently studied in the literature on greedy approximation. In the course of our work, a new property arises naturally and its relation with squeeze symmetric and bidemocratic bases is given. In addition, we study some parameters involving the weak thresholding and Chebyshevian greedy algorithms. Finally, we give examples of conditional bases with some of the weighted greedy-type conditions we study.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2023.53