Characterization of greedy bases in Banach spaces

TL;DR

This paper introduces a new way to characterize greedy and 1-greedy bases in Banach spaces using specific functionals, and proposes a unifying property that enhances understanding of unconditionality and democracy.

Contribution

It provides a novel characterization of greedy bases and a new property linking unconditionality and democracy, improving constant dependencies.

Findings

New characterization of greedy bases using distance-based functionals

Introduction of a unifying property for unconditionality and democracy

Enhanced bounds on constants related to basis properties

Abstract

We shall present a new characterization of greedy bases and 1-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the notions of unconditionality and democracy and allows us to recover a better dependence on the constants.