Weak greedy algorithms and the equivalence between semi-greedy and almost greedy Markushevich bases

BERASATEGUI, MIGUEL; LASSALLE, SILVIA

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS

ROYAL SOC EDINBURGH

Lugar: Edinburgo; Año: 2023

0308-2105

The main purpose of this paper is to study weight-semi-greedy Markushevich bases,and in particular, find conditions under which such bases are weight-almost greedy.In this context, we prove that, for a large class of weights, the two notions areequivalent. We also show that all weight semi-greedy bases are truncationquasi-greedy and weight-superdemocratic. In all of the above cases, we also bring tothe context of weights the weak greedy and Chebyshev greedy algorithms—whichare frequently studied in the literature on greedy approximation. In the course of ourwork, a new property arises naturally and its relation with squeeze symmetric andbidemocratic bases is given. In addition, we study some parameters involving theweak thresholding and Chebyshevian greedy algorithms. Finally, we give examples ofconditional bases with some of the weighted greedy-type conditions we study.