Bidemocratic bases and their connections with other greedy-type bases
From MaRDI portal
Publication:6369041
DOI10.1007/S00365-022-09607-ZarXiv2105.15177MaRDI QIDQ6369041
Pablo M. Berná, José Luis Ansorena, M. Berasategui, F. Albiac, Silvia Lassalle
Publication date: 31 May 2021
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 the space 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 democratic bases.
Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Banach sequence spaces (46B45) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)
This page was built for publication: Bidemocratic bases and their connections with other greedy-type bases
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6369041)
