On the existence of almost greedy bases in Banach spaces

S. J. Dilworth, N. J. Kalton, and Denka Kutzarova. "On the existence of almost greedy bases in Banach spaces." Studia Mathematica 159.1 (2003): 67-101. <http://eudml.org/doc/284737>.

@article{S2003,
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.},
author = {S. J. Dilworth, N. J. Kalton, Denka Kutzarova},
journal = {Studia Mathematica},
keywords = {almost greedy bases; thresholding operators; weakly null sequences; democratic bases; quasi-greedy bases},
language = {eng},
number = {1},
pages = {67-101},
title = {On the existence of almost greedy bases in Banach spaces},
url = {http://eudml.org/doc/284737},
volume = {159},
year = {2003},
}

TY - JOUR
AU - S. J. Dilworth
AU - N. J. Kalton
AU - Denka Kutzarova
TI - On the existence of almost greedy bases in Banach spaces
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 1
SP - 67
EP - 101
AB - 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.
LA - eng
KW - almost greedy bases; thresholding operators; weakly null sequences; democratic bases; quasi-greedy bases
UR - http://eudml.org/doc/284737
ER -