Uniqueness of unconditional basis of H-p(T) ? l(2) and H-p(T) ? T-(2) for 0 p 1

摘要

Our goal in this paper is to advance the state of the art of the topic of uniqueness of unconditional basis. To that end we establish general conditions on a pair (X,Y) formed by a quasi-Banach space X and a Banach space Y which guarantee that every unconditional basis of their direct sum X circle plus Y splits into unconditional bases of each summand. As application of our methods we obtain that, among others, the spaces H-p(T-d)circle plus T-(2) and H-p(T-d)circle plus l(2), for p is an element of(0,1) and d is an element of N, have a unique unconditional basis (up to equivalence and permutation). (C) 2022 The Author(s). Published by Elsevier Inc.