Uniqueness of unconditional bases in c_0-products
Functional Analysis
2007-05-23 v1
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). 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.
Cite
@article{arxiv.math/9811145,
title = {Uniqueness of unconditional bases in c_0-products},
author = {Peter G. Casazza and Nigel J. Kalton},
journal= {arXiv preprint arXiv:math/9811145},
year = {2007}
}
Comments
23 pages; to appear: Studia Math