Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces
Volume 227 / 2015
Studia Mathematica 227 (2015), 133-140
MSC: Primary 41A65; Secondary 41A46, 46B15.
DOI: 10.4064/sm227-2-3
Abstract
We show that in a super-reflexive Banach space, the conditionality constants $k_N(\mathscr B)$ of a quasi-greedy basis $\mathscr B$ grow at most like $O((\log N)^{1-\varepsilon})$ for some $0 < \varepsilon < 1$. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in $L_p$ for $1< p< \infty$. We also give an example of a quasi-greedy basis $\mathscr B$ in a reflexive Banach space with $k_N(\mathscr B)\approx \log N$.
