Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces
Tom 227 / 2015
Studia Mathematica 227 (2015), 133-140
MSC: Primary 41A65; Secondary 41A46, 46B15.
DOI: 10.4064/sm227-2-3
Streszczenie
We show that in a super-reflexive Banach space, the conditionality constants 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.
