Title: Conditional quasi-greedy bases in Hilbert and Banach spaces

Authors: Gustavo Garrigos and Przemyslaw Wojtaszczyk

Issue: Volume 63 (2014), Issue 4, 1017-1036


For quasi-greedy bases $\mathscr{B}$ in Hilbert spaces, we give---answering a question by Temlyakov---an improved bound of the associated conditionality constants $k_N(\mathscr{B})=O(\log N)^{1-\epsilon}$, for some $\epsilon>0$. We show the optimality of this bound with an explicit construction, based on a refinement of the method of Olevskii. This construction leads to other examples of quasi-greedy bases with large $k_N$ in Banach spaces, which are of independent interest.