This is an announcement for the paper "Conditional quasi-greedy bases in Hilbert and Banach spaces" by G. Garrigos and P. Wojtaszczyk.

Abstract: We show that, for quasi-greedy bases in Hilbert spaces, the associated conditionality constants grow at most as $O(\log N)^{1-\epsilon}$, for some $\epsilon>0$, answering a question by Temlyakov. 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.

Archive classification: math.FA math.CA

Submitted from: gustavo.garrigos@uam.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1301.4844

or

http://arXiv.org/abs/1301.4844