Uniqueness of unconditional bases in $c_0$-products
Volume 133 / 1999
Studia Mathematica 133 (1999), 275-294
DOI: 10.4064/sm-133-3-275-294
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 $p_n ￬ 1$, $N_{n+1} ≥ 2N_{n}$ and $(p_n-p_{n+1}) logN_{n}$ remains bounded.
