Weaker forms of unconditionality of bases in greedy approximation

TL;DR

This paper introduces a new class of bases weaker than quasi-greedy bases that still maintain unconditionality properties, offering insights into their approximation capabilities and a new characterization of nearly unconditional bases.

Contribution

It defines a novel class of bases weaker than quasi-greedy, preserving unconditionality and optimality in greedy algorithms, and provides a new characterization of nearly unconditional bases.

Findings

New class of bases weaker than quasi-greedy bases identified.

Characterization of nearly unconditional bases achieved.

Insights into the unconditionality measure of these bases.

Abstract

In this paper we study a new class of bases, weaker than quasi-greedy bases, which retain their unconditionality properties and can provide the same optimality for the thresholding greedy algorithm. We measure how far these bases are from being unconditional and use this concept to give a new characterization of nearly unconditional bases.