Uniqueness of unconditional bases of $c_{0}(l_{p})$, 0 < p < 1

ArticleOriginal scientific text

Title

Authors ^1,²

Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211, U.S.A.
Depto. Matemática e Informática, Universidad Pública de Navarra, C/Sadar, S/n, 31006 Pamplona, Spain.

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} (l ₁)

.

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