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Two Characterizations of the Standard Unit Vector Basis of l1
Positivity, 2003Co-Authors: David MitraAbstract: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 ∞ is equivalent to the Standard Unit Vector basis of l 1.
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two characterizations of the Standard Unit Vector basis of l_1
arXiv: Functional Analysis, 2000Co-Authors: David MitraAbstract: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~$l_1$.