Two characterizations of the standard unit vector basis of l₁

2000/10/12 by David Mitra, Mitra, David
Computer Science · Mathematics · #46B15 (Secondary) #46B45 (Primary) #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46B15 #msc:46B45

paper · pdf · doi:10.48550/arxiv.math/0010128

Latex. 8 pgs

arxiv created 2000/10/12 · openalex publication_date 2000/10/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 l₁. We show that a normalized unconditional basic sequence in l₁ that is semi-normalized in l_∞ is equivalent to the standard unit vector basis of~l₁.

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