Equivalence between almost-greedy and semi-greedy bases

TL;DR

This paper extends the known equivalence between almost-greedy and semi-greedy bases from Banach spaces with finite cotype to all Banach spaces, broadening the applicability of this theoretical result.

Contribution

It proves the equivalence of almost-greedy and semi-greedy bases in general Banach spaces, removing previous restrictions.

Findings

Equivalence holds in all Banach spaces.

Generalizes previous finite cotype results.

Strengthens understanding of basis properties.

Abstract

In [3] it was proved that almost-greedy and semi-greedy bases are equivalent in the context of Banach spaces with finite cotype. In this paper we show this equivalence for general Banach spaces.