On the existence of almost greedy bases in Banach spaces

S. J. Dilworth, N. J. Kalton, Denka Kutzarova

Research output: Contribution to journalArticle

Abstract

We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy bases begun in [3]. We show that almost greedy bases are essentially optimal for n-term approximation when the TGA is modified to include a Chebyshev approximation. We prove that if a Banach space X has a basis and contains a complemented subspace with a symmetric basis and finite cotype then X has an almost greedy basis. We show that c0 is the only ℒ space to have a quasi-greedy basis. The Banach spaces which contain almost greedy basic sequences are characterized.

Original languageEnglish (US)
Pages (from-to)67-101
Number of pages35
JournalStudia Mathematica
Volume159
Issue number1
DOIs
StatePublished - Jan 1 2003

ASJC Scopus subject areas

  • Mathematics(all)

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