Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases
Volume 251 / 2020
Studia Mathematica 251 (2020), 277-288
MSC: Primary 46B45; Secondary 46B25, 46B15, 46B10, 46B07, 41A65.
DOI: 10.4064/sm180910-1-2
Published online: 24 October 2019
Abstract
We settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non-superreflexive mixed-norm sequence space. As a by-product, we give applications to the study of conditional Schauder bases and conditional almost greedy bases in this new class of Banach spaces.
