Characterization of $1$-almost greedy bases
Abstract
This article closes the cycle of characterizations of greedy-like bases in the isometric case initiated in [F. Albiac and P. Wojtaszczyk, Characterization of -greedy bases, J. Approx. Theory 138 (2006)] with the characterization of -greedy bases and continued in [F. Albiac and J. L. Ansorena, Characterization of -quasi-greedy bases, arXiv:1504.04368v1 [math.FA] (2015)] with the characterization of -quasi-greedy bases. Here we settle the problem of providing a characterization of -almost greedy bases in Banach spaces. We show that a (semi-normalized) basis in a Banach space is almost greedy with almost greedy constant equal to if and only if it has Property (A). This fact permits now to state that a basis is -greedy if and only if it is -almost greedy and -quasi-greedy. As a by-product of our work we also provide a tight characterization of almost greedy bases.
Keywords
Cite
@article{arxiv.1506.03397,
title = {Characterization of $1$-almost greedy bases},
author = {F. Albiac and J. L. Ansorena},
journal= {arXiv preprint arXiv:1506.03397},
year = {2015}
}