Approximation spaces, greedy classes and Lorentz spaces

Abstract

We characterize the approximation spaces of a broad class of bases - which includes almost greedy bases - in terms of weighted Lorentz spaces. For those bases, we also find necessary and sufficient conditions under which the approximation spaces and greedy classes are the same.

V4: We fixed some typos, gave more details in the proof of Lemma 4.1 (i), and fixed the last part of Lemma 4.2 (ii)