Weak thresholding greedy algorithms in Banach spaces

S. J. Dilworth, Denka Kutzarova, Th Schlumprecht, P. Wojtaszczyk

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)3900-3921
Number of pages22
JournalJournal of Functional Analysis
Volume263
Issue number12
DOIs
StatePublished - Dec 15 2012

Keywords

  • Banach spaces
  • Greedy approximation
  • Thresholding greedy algorithm
  • Weak thresholding

ASJC Scopus subject areas

  • Analysis

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