Publication: Bidemocratic bases and their connections with other greedy-type bases
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AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095366-B-I00/ES/
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105599GB-I00/ES/
Abstract
In nonlinear greedy approximation theory, bidemocratic bases have traditionally played the role of dualizing democratic, greedy, quasi-greedy, or almost greedy bases. In this article we shift the viewpoint and study them for their own sake, just as we would with any other kind of greedy-type bases. In particular we show that bidemocratic bases need not be quasi-greedy, despite the fact that they retain a strong unconditionality flavor which brings them very close to being quasi-greedy. Our constructive approach gives that for each 1 < p < infinity the space L-p has a bidemocratic basis which is not quasi-greedy. We also present a novel method for constructing conditional quasi-greedy bases which are bidemocratic, and provide a characterization of bidemocratic bases in terms of the new concepts of truncation quasi-greediness and partially demo-cratic bases.
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