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Weaker forms of unconditionality of bases in greedy approximation
Fernando Albiac, Jose L. Ansorena, Miguel Berasategui +2
In this paper we study a new class of bases, weaker than quasi-greedy bases, which retain their unconditionality properties and can provide the same optimality for the thresholding…
Bidemocratic bases and their connections with other greedy-type bases
Fernando Albiac, Jose L. Ansorena, Miguel Berasategui +2
In nonlinear greedy approximation theory, bidemocratic bases have traditionally played the role of dualizing democratic, greedy, quasi-greedy, or almost greedy bases. In this artic…
New parameters and Lebesgue-type estimates in greedy approximation
Fernando Albiac, Jose L. Ansorena, Pablo M. Berna
The purpose of this paper is to quantify the size of the Lebesgue constants associated with the thresholding greedy algorithm in terms of a new generation of…
Strong partially greedy bases and Lebesgue-type inequalities
Miguel Berasategui, Pablo M. Berná, Silvia Lassalle
In this paper we continue the study of Lebesgue-type inequalities for greedy algorithms. We introduce the notion of strong partially greedy Markushevich bases and study the Lebesgu…
Greedy approximation for biorthogonal systems in quasi-Banach spaces
Fernando Albiac, Jose L. Ansorena, Pablo M. Berna +1
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevic…
Lebesgue inequalities for Chebyshev Thresholding Greedy Algorithms
Pablo M. Berná, Oscar Blasco, Gustavo Garrigós +2
We establish estimates for the Lebesgue parameters of the Chebyshev Weak Thresholding Greedy Algorithm in the case of general bases in Banach spaces. These generalize and slightly…