UNIQUENESS OF UNCONDITIONAL BASES OF C0(LP),0-LESS-THAN-P-LESS-THAN-1

We prove that if 0 < p < 1 then a normalized unconditional basis of a complemented subspace of co(l(p)) must be equivalent to a permutation of a subset of the canonical unit vector basis of c0(l(p)). In particular, c0(l(p)) has unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss, and Tzafriri have previously proved the same result for co(l1).