On consecutive greedy and other greedy-like type of bases

TL;DR

This paper explores the properties of consecutive greedy bases and related concepts, providing new characterizations and extending understanding of greedy algorithms in Banach space theory.

Contribution

It introduces and characterizes consecutive greedy bases, offering new insights into almost greedy and squeeze symmetric Schauder bases.

Findings

Characterization of consecutive greedy bases

New criteria for almost greedy and squeeze symmetric bases

Analysis of greedy-like properties with constant 1

Abstract

We continue our study of the Thresholding Greedy Algorithm when we restrict the vectors involved in our approximations so that they either are supported on intervals of $\mathbb N$ or have constant coefficients. We introduce and characterize what we call consecutive greedy bases and provide new characterizations of almost greedy and squeeze symmetric Schauder bases. Moreover, we investigate some cases involving greedy-like properties with constant 1 and study the related notion of Property (A,$\tau$).