arXiv:math/9811145 Abstract

arXiv:math/9811145 [math.FA]Abstract References Reviews Resources

Uniqueness of unconditional bases in c_0-products

Published 1998-11-24Version 1

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.

Comments: 23 pages; to appear: Studia Math

Categories: math.FA

Subjects: 46B15, 46B07

Keywords: unique unconditional basis, unconditional bases, uniqueness, tsirelsons space, simpler proof

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