imprint:
Department of Mathematics of Indiana University, 2014
Published in:Indiana University Mathematics Journal
Language:
English
ISSN:
0022-2518;
1943-5258
Origination:
Footnote:
Description:
<p>For quasi-greedy bases 𝓑 in Hilbert spaces, we give—answering a question by Temlyakov—an improved bound of the associated conditionality constants kN(𝓑) = O(logN)1–ε, for some ε > 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 kN in Banach spaces, which are of independent interest.</p>