Bidemocratic bases and their connections with other greedy-type bases

2021/05/31 by Fernando Albiac, Albiac, Fernando, José L. Ansorena +7 · 1 citation
Computer Science · Decision Sciences · #41A65 (Primary) 41A46 #46B15 #46B45 (Secondary) #Advanced Algebra and Logic #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2105.15177

openalex publication_date 2021/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

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