Uniqueness of unconditional bases in c0-products
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 c0(X). In particular, we show that for Tsirelson's space T, every unconditional basis of c0(T) must be equivalent to a subsequence of the canonical basis but c0(T) still fails to have a unique unconditional basis. We also give some positive results including a simpler proof that c0(l1)has a unique unconditional basis.
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