Weak thresholding greedy algorithms in Banach spaces

We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives th...

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Bibliographic Details
Published in:Journal of functional analysis Vol. 263; no. 12; pp. 3900 - 3921
Main Authors: Dilworth, S.J., Kutzarova, Denka, Schlumprecht, Th, Wojtaszczyk, P.
Format: Journal Article
Language:English
Published: Elsevier Inc 15.12.2012
Subjects:
Banach spaces
Greedy approximation
Thresholding greedy algorithm
Weak thresholding
Thresholding greedy algorithm
Banach spaces
Weak thresholding
Greedy approximation
ISSN:0022-1236, 1096-0783
Online Access:Get full text
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Summary:We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives the best n-term approximation up to a multiplicative constant, then the system is already “greedy”. Similar results are proved for “almost greedy” and “semi-greedy” systems.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2012.09.011