Uniqueness of unconditional basis of H_p(\mathbbT)⊕ℓ₂ and H_p(\mathbbT)\oplusT⁽²⁾ for 0

2020/10/04 by Fernando Albiac, Albiac, Fernando, José L. Ansorena +3
Computer Science · Engineering · Mathematics · #46A16 #46A35 #46A40 #46A45 (Secondary) #46B15 (Primary) 46B20 #46B42 #46B45 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2010.01501

openalex publication_date 2020/10/04 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

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 (\mathbbX, \mathbbY) formed by a quasi-Banach space \mathbbX and a Banach space \mathbbY which guarantee that every unconditional basis of their direct sum \mathbbX⊕\mathbbY splits into unconditional bases of each summand. As application of our methods we obtain that, among others, the spaces H_p(\mathbbT^d) \oplusT⁽²⁾ and H_p(\mathbbT^d)⊕ℓ₂, for p∈(0,1) and d∈ℕ, have a unique unconditional basis (up to equivalence and permutation).

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