Weak convergence of greedy algorithms in banach spaces

S. J. Dilworth, Denka Kutzarova, Karen L. Shuman, V. N. Temlyakov, P. Wojtaszczyk

Research output: Contribution to journalArticlepeer-review

Abstract

We study the convergence of certain greedy algorithms in Banach spaces. We introduce the WN property for Banach spaces and prove that the algorithms converge in the weak topology for general dictionaries in uniformly smooth Banach spaces with the WN property. We show that reflexive spaces with the uniform Opial property have the WN property. We show that our results do not extend to algorithms which employ a 'dictionary dual' greedy step.

Original languageEnglish (US)
Pages (from-to)609-628
Number of pages20
JournalJournal of Fourier Analysis and Applications
Volume14
Issue number5-6
DOIs
StatePublished - Dec 2008
Externally publishedYes

Keywords

  • Greedy algorithms
  • Uniform Opial property
  • Uniformly smooth Banach spaces
  • Weak convergence

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

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