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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Vydané v:Journal of functional analysis Ročník 263; číslo 12; s. 3900 - 3921
Hlavní autori: Dilworth, S.J., Kutzarova, Denka, Schlumprecht, Th, Wojtaszczyk, P.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 15.12.2012
Predmet:
Banach spaces
Greedy approximation
Thresholding greedy algorithm
Weak thresholding
Thresholding greedy algorithm
Banach spaces
Weak thresholding
Greedy approximation
ISSN:0022-1236, 1096-0783
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Popis
Shrnutí: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