4 citations · 7 across the 22 of their papers we have counts for
25 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…
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 García
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…
On sequential greedy-type bases
Miguel Berasategui, Pablo M. Berná, Hung Viet Chu
It is known that a basis is almost greedy if and only if the thresholding greedy algorithm gives essentially the smallest error term compared to errors from projections onto interv…
Approximation by polynomials with constant coefficients and the Thresholding Greedy Algorithm
Miguel Berasategui, Pablo M. Berná, David González
Greedy bases are those bases where the Thresholding Greedy Algorithm (introduced by S. V. Konyagin and V. N. Temlyakov) produces the best possible approximation up to a constant. I…
Linear versus nonlinear forms of partial unconditionality of bases
Fernando Albiac, Jose L. Ansorena, Miguel Berasategui
The main results in this paper contribute to bring to the fore novel underlying connections between the contemporary concepts and methods springing from greedy approximation theory…
On consecutive greedy and other greedy-like type of bases
Miguel Berasategui, Pablo M. Berná, Hung Viet Chu
We continue our study of the Thresholding Greedy Algorithm when we restrict the vectors involved in our approximations so that they either are supported on intervals of …
Elton's near unconditionality of bases as a threshold-free form of greediness
Fernando Albiac, José L. Ansorena, Miguel Berasategui
Elton's near unconditionality and quasi-greediness for largest coefficients are two properties of bases that made their appearance in functional analysis from very different areas…
Extensions and new characterizations of some greedy-type bases
Miguel Berasategui, Pablo M. Berná, Hung Viet Chu
Partially greedy bases in Banach spaces were introduced by Dilworth et al. as a strictly weaker notion than the (almost) greedy bases. In this paper, we study two natural ways to s…
Sparse approximation using new greedy-like bases in superreflexive spaces
Fernando Albiac, Jose L. Ansorena, Miguel Berasategui
This paper is devoted to theoretical aspects on optimality of sparse approximation. We undertake a quantitative study of new types of greedy-like bases that have recently arisen in…
Extensions of democracy-like properties for sequences with gaps
Miguel Berasategui, Pablo M. Berná
In \cite{O2015}, T. Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps. In this paper, we extend some of the notions that app…
Weak weight-semi-greedy Markushevich bases
Miguel Berasategui, Silvia Lassalle
We introduce and study the notion of weak weight-semi-greedy Markushevich bases - which extends the concepts of weight semi-greedy and weak semi-greedy Markushevich bases. In parti…
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…
Greedy-like bases for sequences with gaps
Miguel Berasategui, Pablo M. Berná
In [25], T. Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the --quasi-greedy property tha…
Quasi-greedy bases for sequences with gaps
Miguel Berasategui, Pablo M. Berná
In this paper, we establish new advances in the theory started by T. Oikhberg in [15] where the author joins greedy approximation theory with the use of sequences with gaps. Concre…
Weak greedy algorithms and the equivalence between semi-greedy and almost greedy Markushevich bases
Miguel Berasategui, Silvia Lassalle
We introduce and study the notion of weak semi-greedy systems -which is inspired in the concepts of semi-greedy and Branch semi-greedy systems and weak thresholding sets-, and prov…
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…