TY - JOUR
T1 - Weak thresholding greedy algorithms in Banach spaces
AU - Dilworth, S. J.
AU - Kutzarova, Denka
AU - Schlumprecht, Th
AU - Wojtaszczyk, P.
N1 - \u2729 The first author was partially supported by NSF grants DMS 0701552 and DMS 1101490, the third author was supported by NSF grant DMS 0856148, and the fourth author was supported by Polish MNiSW grant N201 269335 and EU project POWIEW. All authors were supported by the Workshop in Analysis and Probability at Texas A&M University in 2011. * Corresponding author. E-mail addresses: [email protected] (S.J. Dilworth), [email protected] (D. Kutzarova), [email protected] (Th. Schlumprecht), [email protected] (P. Wojtaszczyk). 1 Current address: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. 2 Current address: Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, ul. Prosta 69, 02-838 Warszawa, Poland.
PY - 2012/12/15
Y1 - 2012/12/15
N2 - 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.
AB - 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.
KW - Banach spaces
KW - Greedy approximation
KW - Thresholding greedy algorithm
KW - Weak thresholding
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U2 - 10.1016/j.jfa.2012.09.011
DO - 10.1016/j.jfa.2012.09.011
M3 - Article
AN - SCOPUS:84868207995
SN - 0022-1236
VL - 263
SP - 3900
EP - 3921
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 12
ER -