5 papers · 1 filter
When Greedy Approximation Breaks: Counterexamples in Quasi-Banach Spaces
Fernando Albiac, José L. Ansorena, Miguel Berasategui +1
We construct two counterexamples that resolve long-standing open problems on greedy approximation theory with respect to bases, posed in [F. Albiac et al., Dissertationes Math. 560…
Lebesgue-type estimates for greedy algorithms in quasi-Banach spaces
Miguel Berasategui, Pablo M. Berná, Hung Viet Chu +1
We continue the study of Lebesgue-type parameters for various greedy algorithms in quasi-Banach spaces. First, we introduce a parameter that can be used with the quasi-greedy param…
Summability Methods for the Greedy Algorithm in Banach spaces
Miguel Berasategui, Pablo M. Berná, Stephen J. Dilworth +1
For the past 25 years, one of the most studied algorithms in the field of Nonlinear Approximation Theory has been the Thresholding Greedy Algorithm. In this paper, we propose new s…
Approximation spaces, greedy classes and Lorentz spaces
Miguel Berasategui, Pablo M. Berná, Andrea GarcÃa
We characterize the approximation spaces of a broad class of bases - which includes almost greedy bases - in terms of weighted Lorentz spaces. For those bases, we also find necessa…
Conditional bases with Property~(A)
Fernando Albiac, Jose L. Ansorena, Pablo Berná +1
Property~(A) is a week symmetry condition that plays a fundamental role in the characterization of greedy-type bases in the isometric case, i.e., when the constants involved in the…