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

David Mitra

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

Functional Analysis 2007-05-23 v1

Authors: David Mitra

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~ $l_1$ .

Keywords

banach space unit vector basis l1 perturbation unconditional basic sequence

Cite

@article{arxiv.math/0010128,
  title  = {Two characterizations of the standard unit vector basis of $l_1$},
  author = {David Mitra},
  journal= {arXiv preprint arXiv:math/0010128},
  year   = {2007}
}

Comments

Latex. 8 pgs

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