# Greedy approximation for biorthogonal systems in quasi-Banach spaces

## TL;DR

This paper extends the theory of greedy algorithms for biorthogonal systems in quasi-Banach spaces, providing new characterizations and properties that deepen understanding of basis approximation in these spaces.

## Contribution

It offers the first systematic study and new characterizations of greedy, quasi-greedy, and almost greedy bases in quasi-Banach spaces.

## Key findings

- Extended characterizations of greedy bases in quasi-Banach spaces
- New properties and relations among basis types identified
- Framework applicable to a broad class of biorthogonal systems

## Abstract

The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) in quasi-Banach spaces from a functional-analytic point of view. We revisit the concepts of greedy, quasi-greedy, and almost greedy bases in this comprehensive framework and provide the (nontrivial) extensions of the corresponding characterizations of those types of bases. As a by-product of our work, new properties arise, and the relations amongst them are carefully discussed.