Non-linear approximation by 1-greedy bases

Abstract

The theory of greedy-like bases started in 1999 when S.V. Konyagin and V.N. Temlyakov introduced in [12] the famous Thresholding Greedy Algorithm. Since this year, different greedy-like bases appeared in the literature, as for instance: quasi-greedy, almost-greedy and greedy bases. The purpose of this paper is to provide a new characterization of 1-greedy bases in terms of the best approximation error of order 1 where we will use the so-called Property (Q⁎) with constant 1 ([5]) to achieve this. Moreover, different connections between some well known notions as unconditionality and symmetry for largest coefficients are studied in our context.