2017/12/11 by Fernando Albiac, Albiac, Fernando, José L. Ansorena +1
Computer Science · Mathematics · #46B15 (Primary) 41A65 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1712.04004
openalex publication_date 2017/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that for a conditional quasi-greedy basis \B in a\nBanach space mathbbX, the associated sequence\n(km[\B])m=1\∞ of its conditionality constants verifies\nthe estimate km[\B]=\O(\log m) and that if the reverse\ninequality \log m =\O(km[\B]) holds then mathbbX is\nnon-superreflexive. However, in the existing literature one finds very few\ninstances of non-superreflexive spaces possessing quasi-greedy basis with\nconditionality constants as large as possible. Our goal in this article is to\nfill this gap. To that end we enhance and exploit a combination of techniques\ndeveloped independently, on the one hand by Garrig 'os and Wojtaszczyk in\n[Conditional quasi-greedy bases in Hilbert and Banach spaces, Indiana Univ.\nMath. J. 63 (2014), no. 4, 1017-1036] and, on the other hand, by Dilworth et\nal. in [On the existence of almost greedy bases in Banach spaces, Studia Math.\n159 (2003), no. 1, 67-101], and craft a wealth of new examples of\nnon-superreflexive classical Banach spaces having quasi-greedy bases\n\B with km[\B]=\O(\log m).\n