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

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

2000-10-12

arxiv.org/abs/math/0010128v1

Mathematics

Functional Analysis

Latex. 8 pgs

Scientific paper

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~$l_1$.

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