%0 Journal Article
%T Uniqueness of unconditional bases in c_0-products
%A Peter G. Casazza
%A Nigel J. Kalton
%J Mathematics
%D 1998
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/9811145v1