Uniqueness of unconditional bases in $c_0$-products

P. Casazza; N. Kalton

ArticleOriginal scientific text

Title

Uniqueness of unconditional bases in $c_{0}$ -products

Authors ¹, ¹

Affiliations

Department of Mathematics, University of Missouri, Columbia, Missouri 65211, U.S.A.

Abstract

We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does

c_{0} (X)

. We also give some positive results including a simpler proof that

c_{0} (ℓ_{1})

has a unique unconditional basis and a proof that

c_{0} (ℓ_{p_{n}}^{N_{n}})

has a unique unconditional basis when

p_{n} ￬ 1

,

N_{n + 1} \geq 2 N_{n}

and

(p_{n} - p_{n + 1}) {\log N}_{n}

remains bounded.

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Title

Uniqueness of unconditional bases in c0-products

Affiliations

Abstract

Bibliography

Uniqueness of unconditional bases in $c_{0}$ -products