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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## On the existence of almost greedy bases in Banach spaces

### Tom 159 / 2003

Studia Mathematica 159 (2003), 67-101 MSC: Primary 46B15; Secondary 41A65, 46B20. DOI: 10.4064/sm159-1-4

#### Streszczenie

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 $c_0$ is the only ${\mathcal L}_\infty$ space to have a quasi-greedy basis. The Banach spaces which contain almost greedy basic sequences are characterized.

#### Autorzy

• S. J. DilworthDepartment of Mathematics
University of South Carolina
Columbia, SC 29208, U.S.A.
e-mail
• N. J. KaltonDepartment of Mathematics
University of Missouri
Columbia, MO 65211, U.S.A.
e-mail
• Denka KutzarovaInstitute of Mathematics
Sofia, Bulgaria
and
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801, U.S.A.
e-mail

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