A functional characterization of almost greedy and partially greedy bases

TL;DR

This paper provides a new functional characterization of almost-greedy and partially-greedy bases in Banach spaces, building on previous concepts of quasi-greediness, democracy, and conservativeness.

Contribution

It introduces a novel functional characterization of these bases, extending the understanding of their structure in general Banach spaces.

Findings

New functional characterization of almost-greedy bases

Extension of characterization to partially-greedy bases

Deeper understanding of basis properties in Banach spaces

Abstract

In 2003, S. J. Dilworth et al. ([8]) introduced the notion of almost-greedy (resp. partially-greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (resp. conservativeness). In this paper we will show a new functional characterization of these type of bases in general Banach spaces following the spirit of the characterization of greediness proved in [5].