We prove that if 0 < p < 1 then a normalized unconditional basis of a complemented subspace of must be equivalent to a permutation of a subset of the canonical unit vector basis of . In particular, has unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss, and Tzafriri have previously proved the same result for .
@article{bwmeta1.element.bwnjournal-article-smv102i3p193bwm,
author = {C. Ler\'anoz},
title = {Uniqueness of unconditional bases of $c\_{0}(l\_{p})$, 0 < p < 1},
journal = {Studia Mathematica},
volume = {103},
year = {1992},
pages = {193-207},
zbl = {0812.46003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv102i3p193bwm}
}
Leránoz, C. Uniqueness of unconditional bases of $c_{0}(l_{p})$, 0 < p < 1. Studia Mathematica, Tome 103 (1992) pp. 193-207. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv102i3p193bwm/
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