This is an announcement for the paper "Characterization of $1$-almost greedy bases" by F. Albiac and J. L. Ansorena.
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 $1$-greedy bases, J. Approx. Theory 138 (2006)] with the characterization of $1$-greedy bases and continued in [F. Albiac and J. L. Ansorena, Characterization of $1$-quasi-greedy bases, arXiv:1504.04368v1 [math.FA] (2015)] with the characterization of $1$-quasi-greedy bases. Here we settle the problem of providing a characterization of $1$-almost greedy bases in (real or complex) Banach spaces. We show that a (semi-normalized) basis in a Banach space is almost-greedy with almost greedy constant equal to $1$ if and only if it is quasi-greedy with suppression quasi-greedy constant equal to $1$ and has Property (A).
Archive classification: math.FA
Mathematics Subject Classification: 46B15 (Primary) 41A65, 46B15 (Secondary)
Submitted from: joseluis.ansorena@unirioja.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.03397
or