Uniqueness of unconditional basis of 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.
