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

David Mitra

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

David Mitra

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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~$l_1$.

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David Mitra. 2000-10-12. Two characterizations of the standard unit vector basis of $l_1$. https://arxiv.org/abs/math/0010128

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