10 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…
Lipschitz extensions into -Banach spaces, and canonical embeddings of Lipschitz-free -spaces for
Fernando Albiac, José L. Ansorena
We show that inclusions of -metric spaces always produce genuine linear embeddings at the level of Lipschitz-free -spaces. More precisely, for every and every inclusi…
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…
Unconditional structure of Banach spaces with few operators
Fernando Albiac, Jose L. Ansorena
This article was initially motivated by our goal to show that the Banach space constructed by Gowers in [W. T. Gowers, A solution to Banach's hyperplane problem, Bull.…
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…
On Banach envelopes and duals of Lipschitz-free -spaces for
Fernando Albiac, Jose L. Ansorena
With the aim to better understand the intricate geometry of the class of Lipschitz free -spaces when , in this note we study their Banach env…