Weak weight-semi-greedy Markushevich bases

TL;DR

This paper introduces and analyzes weak weight-semi-greedy Markushevich bases, exploring their properties, conditions for weight almost greediness, and relationships with other greedy basis concepts.

Contribution

It extends the theory of greedy bases by defining weak weight-semi-greedy Markushevich bases and establishing their equivalence with weak weight almost greedy bases.

Findings

Weak weight-semi-greedy Markushevich bases are introduced and characterized.

Conditions for such bases to be weight almost greedy are identified.

Weak weight almost greedy bases are shown to be equivalent to weight almost greedy bases.

Abstract

We introduce and study the notion of weak weight-semi-greedy Markushevich bases - which extends the concepts of weight semi-greedy and weak semi-greedy Markushevich bases. In particular, we study conditions under which such bases are weight almost greedy. We also define the notion of weak weight almost greedy bases, and prove that this formally weaker concept is equivalent to that concept of weight almost greedy bases. Finally, we study some parameters involving the weak thresholding and Chebyshevian greedy algorithms.