Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces

F. Albiac, et al. "Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces." Studia Mathematica 227.2 (2015): 133-140. <http://eudml.org/doc/285579>.

@article{F2015,
abstract = {We show that in a super-reflexive Banach space, the conditionality constants $k_\{N\}(ℬ)$ of a quasi-greedy basis ℬ grow at most like $O((log N)^\{1-ε\})$ for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in $L_\{p\}$ for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with $k_\{N\}(ℬ) ≈ log N$.},
author = {F. Albiac, J. L. Ansorena, G. Garrigós, E. Hernández, M. Raja},
journal = {Studia Mathematica},
keywords = {conditional basis; quasi-greedy basis; thresholding greedy algorithm; uniform convexity; weak parallelogram inequality; reflexive space; super-reflexive space},
language = {eng},
number = {2},
pages = {133-140},
title = {Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces},
url = {http://eudml.org/doc/285579},
volume = {227},
year = {2015},
}

TY - JOUR
AU - F. Albiac
AU - J. L. Ansorena
AU - G. Garrigós
AU - E. Hernández
AU - M. Raja
TI - Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces
JO - Studia Mathematica
PY - 2015
VL - 227
IS - 2
SP - 133
EP - 140
AB - We show that in a super-reflexive Banach space, the conditionality constants $k_{N}(ℬ)$ of a quasi-greedy basis ℬ grow at most like $O((log N)^{1-ε})$ for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in $L_{p}$ for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with $k_{N}(ℬ) ≈ log N$.
LA - eng
KW - conditional basis; quasi-greedy basis; thresholding greedy algorithm; uniform convexity; weak parallelogram inequality; reflexive space; super-reflexive space
UR - http://eudml.org/doc/285579
ER -