Lebesgue inequalities for Chebyshev thresholding greedy algorithms

We establish estimates for the Lebesgue parameters of the Chebyshev weak thresholding greedy algorithm in the case of general bases in Banach spaces. These generalize and slightly improve earlier results in Dilworth et al. (Rev Mat Complut 28(2):393–409, 2015), and are complemented with examples sho...

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Bibliographic Details
Published in:Revista matemática complutense Vol. 33; no. 3; pp. 695 - 722
Main Authors: Berná, P. M., Blasco, Ó., Garrigós, G., Hernández, E., Oikhberg, T.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.09.2020
Springer Nature B.V
Subjects:
Algebra
Analysis
Applications of Mathematics
Banach spaces
Chebyshev approximation
Geometry
Greedy algorithms
Mathematics
Mathematics and Statistics
Parameter estimation
Topology
41A46
46B15
41A65
Quasi-greedy basis
Thresholding greedy algorithm
Semi-greedy bases
Thresholding Chebyshev greedy algorithm
ISSN:1139-1138, 1988-2807
Online Access:Get full text
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Summary:We establish estimates for the Lebesgue parameters of the Chebyshev weak thresholding greedy algorithm in the case of general bases in Banach spaces. These generalize and slightly improve earlier results in Dilworth et al. (Rev Mat Complut 28(2):393–409, 2015), and are complemented with examples showing the optimality of the bounds. Our results also clarify certain bounds recently announced in Shao and Ye (J Inequal Appl 2018(1):102, 2018), and answer some questions left open in that paper.
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ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-019-00328-9