On the existence of almost greedy bases in Banach spaces

• Autorzy: S. J. Dilworth , N. J. Kalton , Denka Kutzarova
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 46B20: Geometry and structure of normed linear spaces
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 1
• Strony: 67-101

Daty

wydano

2003

Twórcy

autor

S. J. Dilworth

• Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.

autor

N. J. Kalton

• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.

autor

Denka Kutzarova

• Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria
• Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.

Identyfikatory

DOI

10.4064/sm159-1-4