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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Published inRevista matemática complutense Vol. 30; no. 2; pp. 369 - 392
Main Authors Berná, Pablo M., Blasco, Óscar, Garrigós, Gustavo
Format Journal Article
LanguageEnglish
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
Online AccessGet full text
ISSN1139-1138
1988-2807
DOI10.1007/s13163-017-0221-x

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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.
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ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-017-0221-x