Uniqueness of unconditional basis of $\ell _{p}(c_{0})$ and $\ell _{p}(\ell _{2})$, $0< p< 1$
Volume 150 / 2002
Studia Mathematica 150 (2002), 35-52
MSC: 46A16, 46A35, 46A40, 46A45.
DOI: 10.4064/sm150-1-4
Abstract
We prove that the quasi-Banach spaces $\ell _{p}(c_{0})$ and $\ell _{p}(\ell _{2})$ ($0< p< 1$) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes $\ell _{1}(c_{0})$ and $\ell _{1}(\ell _{2})$. They used duality techniques which are not available in the non-locally convex case.
