Greedy Algorithm for General Biorthogonal Systems

We consider biorthogonal systems in quasi-Banach spaces such that the greedy algorithm converges for each x∈X (quasi-greedy systems). We construct quasi-greedy conditional bases in a wide range of Banach spaces. We also compare the greedy algorithm for the multidimensional Haar system with the optim...

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Bibliographic Details
Published inJournal of approximation theory Vol. 107; no. 2; pp. 293 - 314
Main Author Wojtaszczyk, P.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2000
Subjects
biorthogonal system
conditional basis
Haar system
quasi-greedy basis
conditional basis
Haar system
quasi-greedy basis
biorthogonal system
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ISSN0021-9045
1096-0430
DOI10.1006/jath.2000.3512

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Summary:We consider biorthogonal systems in quasi-Banach spaces such that the greedy algorithm converges for each x∈X (quasi-greedy systems). We construct quasi-greedy conditional bases in a wide range of Banach spaces. We also compare the greedy algorithm for the multidimensional Haar system with the optimal m-term approximation for this system. This substantiates a conjecture by Temlyakov.
ISSN:0021-9045
1096-0430
DOI:10.1006/jath.2000.3512