New characterizations of the unit vector basis of $c_0$ or $\ell_p$

TL;DR

This paper extends Altshuler's characterization of the unit vector basis in classical sequence spaces to democratic and bidemocratic bases, and provides a new characterization for the $\, ext{l}_1$ basis.

Contribution

It offers new characterizations of the unit vector basis in sequence spaces among democratic and bidemocratic bases, expanding the understanding of basis structures.

Findings

Characterizations among democratic bases

Characterizations among bidemocratic bases

Separate characterization of the $\, ext{l}_1$ basis

Abstract

Motivated by Altshuler's famous characterization of the unit vector basis of $c_0$ or $\ell_p$ among symmetric bases, we obtain similar characterizations among democratic bases and among bidemocratic bases. We also prove a separate characterization of the unit vector basis of $\ell_1$.