F. Albiac, J. L. Ansorena
Published 2015-06-10Version 1
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).
Minimality, homogeneity and topological 0-1 laws for subspaces of a Banach space
The Littlewood--Paley--Rubio de Francia property of a Banach space for the case of equal intervals
Embedding $\ell_{\infty}$ into the space of all Operators on Certain Banach Spaces
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