Two characterizations of the standard unit vector basis of $l_1$

Abstract

We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the unit vector basis of $l_1$. We show that a normalized unconditional basic sequence in $l_1$ that is semi-normalized in $l_{\infty }$ is equivalent to the standard unit vector basis of~$l_1$.

Latex. 8 pgs