Strong Partially Greedy Bases and Lebesgue-Type Inequalities

Abstract

In this paper we continue the study of Lebsgue-type inequalities for greedy algorithms. We introduce the notion of strong partially greedy Markushevich bases and study the Lebesgue-type parameters associated with them. We prove that this property is equivalent to that of being conservative and quasi-greedy, extending a similar result given in the paper by Dilworth, Kalton, Kutzarova and temlyakov (2003) for Schauder bases. We also give a characterization of 1-strong partial greediness, following the study started by Albianc ans Wojtaszczyk (2006) and continued by Albiac and Ansorena (2017).