9 papers
Boundedness of the averaging projections in nonlocally convex Lorentz sequence spaces and applications to basis theory
Fernando Albiac, José L. Ansorena, Miguel Berasategui
We study the boundedness of averaging projections associated with symmetric Schauder bases in quasi-Banach spaces. Although this property is standard in the Banach setting, it is f…
Isometric renormings for greedy bases in Banach spaces, with applications to the Haar System in ,
Fernando Albiac, José L. Ansorena, Miguel Berasategui +1
We investigate the problem of improving the greedy-type constant of a basis by means of an equivalent renorming of the ambient Banach space. Our main result shows that if a Banach…
Dictionary-Restricted First-Order Descent Methods: Bounds and Convergence Rates
Miguel Berasategui, Pablo M. Berná, Antonio Falcó
This paper develops a general theory for first-order descent methods whose search directions are restricted to a prescribed dictionary in a reflexive Banach space. Instead of assum…
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…
Quasi-greedy Markushevich bases, duality and norming subspaces
Miguel Berasategui
We prove that if is a quasi-greedy Markushevich basis of a Banach space , its dual basis spans a norming subspace of . We al…
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…