Two characterizations of the standard unit vector basis of $l_1$
Abstract
Description
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
Latex. 8 pgs