Abstract
It is known that for a conditional quasi-greedy basis B in a Banach space X, the associated sequence (km[B])m=1 ∞ of its conditionality constants verifies the estimate km[B]=O(logm) and that if the reverse inequality logm=O(km[B]) holds then X is non-superreflexive. Indeed, it is known that a quasi-greedy basis in a superreflexive quasi-Banach space fulfils the estimate km[B]=O(logm)1−ϵ for some ϵ>0. However, in the existing literature one finds very few instances of spaces possessing quasi-greedy basis with conditionality constants “as large as possible.” Our goal in this article is to fill this gap. To that end we enhance and exploit a technique developed by Dilworth et al. in [15] and craft a wealth of new examples of both non-superreflexive classical Banach spaces having quasi-greedy bases B with km[B]=O(logm) and superreflexive classical Banach spaces having for every ϵ>0 quasi-greedy bases B with km[B]=O(logm)1−ϵ. Moreover, in most cases those bases will be almost greedy.
Original language | English (US) |
---|---|
Pages (from-to) | 1893-1924 |
Number of pages | 32 |
Journal | Journal of Functional Analysis |
Volume | 276 |
Issue number | 6 |
DOIs | |
State | Published - Mar 15 2019 |
Keywords
- Almost greedy basis
- Conditionality constants
- Quasi-greedy basis
- Subsymmetric basis
ASJC Scopus subject areas
- Analysis