14 papers
A semi-greedy Markushevich basis which is not quasi-greedy
Pablo M. Berná
We construct a quasi-Banach space with a semi-greedy Markushevich basis which is not quasi-greedy, and hence not almost greedy. This gives a negative answer to the question of whet…
Non-linear approximation by -greedy bases
Pablo M. Berná, David González
The theory of greedy-like bases started in 1999 when S. V. Konyagin and V. N. Temlyakov introduced in \cite{KT} the famous Thresholding Greedy Algorithm. Since this year, different…
Universality for non-linear convex variational problems
Pablo M. Berná, Antonio Falcó
This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile…
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…
On Approximation Spaces and Greedy-type Bases
Pablo M. Berná, Hung Viet Chu, Eugenio Hernández
The purpose of this paper is to introduce -Chebyshev-greedy and -partially greedy approximation classes and to study their relation with -approximation spaces, where the l…
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…