Conditional quasi-greedy bases in Hilbert and Banach spaces
Gustavo GarrigosPrzemyslaw Wojtaszczyk
41A6541A4646B15thresholding greedy algorithmquasi-greedy basisconditional basis
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.
Indiana University Mathematics Journal
2014
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10.1512/iumj.2014.63.5269
10.1512/iumj.2014.63.5269
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Indiana Univ. Math. J. 63 (2014) 1017 - 1036
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