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arXiv · 1301.4844

Conditional quasi-greedy bases in Hilbert and Banach spaces

G. Garrigos·P. Wojtaszczyk
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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.

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BibTeXRIS

G. Garrigos, P. Wojtaszczyk. 2013-01-21. Conditional quasi-greedy bases in Hilbert and Banach spaces. https://arxiv.org/abs/1301.4844

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