Uniqueness of unconditional bases of $c_{0}(l_{p})$, 0 < p < 1
Volume 102 / 1992
Studia Mathematica 102 (1992), 193-207
DOI: 10.4064/sm-102-3-193-207
Abstract
We prove that if 0 < p < 1 then a normalized unconditional basis of a complemented subspace of $c_0(l_p)$ must be equivalent to a permutation of a subset of the canonical unit vector basis of $c_0(l_p)$. In particular, $c_0(l_p)$ has unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss, and Tzafriri have previously proved the same result for $c_0(l₁)$.
