Uniqueness of unconditional bases in c_0-products

Details Uniqueness of unconditional bases in c_0-products Uniqueness of unconditional bases in c_0-products

1998-11-24

arxiv.org/abs/math/9811145v1

Mathematics

Functional Analysis

23 pages; to appear: Studia Math

Scientific paper

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). In particular, we show that for Tsirelson's space T, every unconditional basis of c_0(T) must be equivalent to a subsequence of the canonical basis but c_0(T) still fails to have a unique unconditional basis. We also give some positive results including a simpler proof that c_0(l_1)has a unique unconditional basis.

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