Lebesgue inequalities for the greedy algorithm in general bases

We present various estimates for the Lebesgue type inequalities associated with the thresholding greedy algorithm, in the case of general bases in Banach spaces. We show the optimality of the involved constants in some situations. Our results recover and slightly improve various estimates appearing...

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Bibliographic Details
Published in:Revista matemática complutense Vol. 30; no. 2; pp. 369 - 392
Main Authors: Berná, Pablo M., Blasco, Óscar, Garrigós, Gustavo
Format: Journal Article
Language:English
Published: Milan Springer Milan 01.05.2017
Springer Nature B.V
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Greedy algorithms
Inequalities
Mathematics
Mathematics and Statistics
Topology
Quasi-greedy basis
41A46
46B15
Thresholding greedy algorithm
Conditional basis
41A65
ISSN:1139-1138, 1988-2807
Online Access:Get full text
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Summary:We present various estimates for the Lebesgue type inequalities associated with the thresholding greedy algorithm, in the case of general bases in Banach spaces. We show the optimality of the involved constants in some situations. Our results recover and slightly improve various estimates appearing earlier in the literature.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-017-0221-x