F. Albiac

activity

20122026

most citedLipschitz free spaces isomorphic to their infinite sums and geometric applications

26 citations · 87 across the 47 of their papers we have counts for

collaborators

53 papers

math.FA2026

Isometries without linear shadows: failure of Figiel's theorem beyond local convexity

Fernando Albiac, José L. Ansorena, Marek Cúth

A classical theorem of Figiel asserts that every isometric embedding $φ : X \to Y$ between real Banach spaces, with $φ (0) = 0$ , admits a linear contractive left inverse on the clo…

math.FA2026

Differentiability of Lipschitz curves in $p$ -Banach spaces

Fernando Albiac, José L. Ansorena, Pietro Wald

The problem of differentiating Lipschitz curves in Banach spaces goes back to Tamarkin in the early 1930s and is one of the origins of the Radon--Nikodým property in classical Bana…

math.FA2026

Structural consequences of the Schur $p$ -property for Lipschitz-free $p$ -spaces

Fernando Albiac, José L. Ansorena, Marek Cúth

Let $0 < p < q \leq 1$ . We show that the Schur $p$ -property provides a powerful structural principle for Lipschitz-free $p$ -spaces. Our main result asserts that $F_{p} (M)$ has t…

math.FA2026

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…

math.FA2026

Lipschitz extensions into $p$ -Banach spaces, and canonical embeddings of Lipschitz-free $p$ -spaces for $0 < p < 1$

Fernando Albiac, José L. Ansorena

We show that inclusions of $p$ -metric spaces always produce genuine linear embeddings at the level of Lipschitz-free $p$ -spaces. More precisely, for every $0 < p < 1$ and every inclusi…

math.FA2026

Isometric renormings for greedy bases in Banach spaces, with applications to the Haar System in $L_{p} [0, 1]$ , $1 < p < \infty$

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…

math.FA2026

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 $G$ constructed by Gowers in [W. T. Gowers, A solution to Banach's hyperplane problem, Bull.…

math.FA2025

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…

math.FA2025

On Banach envelopes and duals of Lipschitz-free $p$ -spaces for $0 < p < 1$

Fernando Albiac, Jose L. Ansorena

With the aim to better understand the intricate geometry of the class of Lipschitz free $p$ -spaces $F_{p} (M)$ when $0 < p < 1$ , in this note we study their Banach env…

math.FA2025

Lipschitz free $p$ -spaces for $0 < p < 1$ in the light of the Schur $p$ -property and the compact reduction

Fernando Albiac, José L. Ansorena, Jan Bíma +1

The geometric analysis of non-locally convex quasi-Banach spaces presents rich and nuanced challenges. In this paper, we introduce the Schur $p$ -property and the strong Schur $p$ -p…

math.FA2024

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…

math.FA2024★ 1 cited

Isomorphisms between vector-valued $H_{p}$ -spaces for $0 < p \leq 1$ and uniqueness of unconditional structure

Fernando Albiac, Jose L. Ansorena

The aim of this paper is twofold. On the one hand, we manage to identify Banach-valued Hardy spaces of analytic functions over the disc $D$ with other classes of Hardy spa…

math.FA2024

Twenty-five years of greedy bases

Fernando Albiac, Jose L. Ansorena, Vladimir Temlyakov

Although the basic idea behind the concept of a greedy basis had been around for some time, the formal development of a theory of greedy bases was initiated in 1999 with the public…

math.FA2023

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…

math.FA2023

Counterexamples in isometric theory of symmetric and greedy bases

Fernando Albiac, Jose L. Ansorena, Oscar Blasco +2

We continue the study initiated in [F. Albiac and P. Wojtaszczyk, Characterization of $1$ -greedy bases, J. Approx. Theory 138 (2006), no. 1, 65-86] of properties related to greedy…

math.FA2022

The structure of greedy-type bases in Tsirelson's space and its convexifications

Fernando Albiac, José L. Ansorena

Tsirelson's space $T$ made its appearance in Banach space theory in 1974 soon to become one of the most significant counterexamples in the theory. Its structure broke the…

math.FA2022

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…

math.FA2022

Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including Besov spaces

Fernando Albiac, José L. Ansorena, Glenier Bello +1

We prove that the sequence spaces $ℓ_{p} \oplus ℓ_{q}$ and the spaces of infinite matrices $ℓ_{p} (ℓ_{q})$ , $ℓ_{q} (ℓ_{p})$ and $(⨁_{n = 1}^{\infty} ℓ_{p}^{n})_{ℓ_{q}}$ , whic…

math.FA2022

Democracy of quasi-greedy bases in $p$ -Banach spaces with applications to the efficiency of the TGA in the Hardy spaces $H_{p} (D^{d})$

Fernando Albiac, José L. Ansorena, Glenier Bello

We use new methods, specific of non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a $p$ -Banach space for $0 < p < 1$ are democratic. The novel techn…

math.FA2022

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…

math.FA2021★ 1 cited

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…

math.FA2021

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…

math.FA2021

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 $(L_{m})_{m = 1}^{\infty}$ associated with the thresholding greedy algorithm in terms of a new generation of…

math.FA2021

Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces

Fernando Albiac, Jose L. Ansorena

This paper is devoted to providing a unifying approach to the study of the uniqueness of unconditional bases, up to equivalence and permutation, of infinite direct sums of quasi-Ba…

Isometries without linear shadows: failure of Figiel's theorem beyond local convexity

Differentiability of Lipschitz curves in p-Banach spaces

Structural consequences of the Schur p-property for Lipschitz-free p-spaces

Boundedness of the averaging projections in nonlocally convex Lorentz sequence spaces and applications to basis theory

Lipschitz extensions into p-Banach spaces, and canonical embeddings of Lipschitz-free p-spaces for 0<p<1

Isometric renormings for greedy bases in Banach spaces, with applications to the Haar System in Lp​[0,1], 1<p<∞

Unconditional structure of Banach spaces with few operators

When Greedy Approximation Breaks: Counterexamples in Quasi-Banach Spaces

On Banach envelopes and duals of Lipschitz-free p-spaces for 0<p<1

Lipschitz free p-spaces for 0<p<1 in the light of the Schur p-property and the compact reduction

Conditional bases with Property~(A)

Isomorphisms between vector-valued Hp​-spaces for 0<p≤1 and uniqueness of unconditional structure

Twenty-five years of greedy bases

Linear versus nonlinear forms of partial unconditionality of bases

Counterexamples in isometric theory of symmetric and greedy bases

The structure of greedy-type bases in Tsirelson's space and its convexifications

Elton's near unconditionality of bases as a threshold-free form of greediness

Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including Besov spaces

Democracy of quasi-greedy bases in p-Banach spaces with applications to the efficiency of the TGA in the Hardy spaces Hp​(Dd)

Sparse approximation using new greedy-like bases in superreflexive spaces

Weaker forms of unconditionality of bases in greedy approximation

Bidemocratic bases and their connections with other greedy-type bases

New parameters and Lebesgue-type estimates in greedy approximation

Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces

Differentiability of Lipschitz curves in $p$ -Banach spaces

Structural consequences of the Schur $p$ -property for Lipschitz-free $p$ -spaces

Lipschitz extensions into $p$ -Banach spaces, and canonical embeddings of Lipschitz-free $p$ -spaces for $0 < p < 1$

Isometric renormings for greedy bases in Banach spaces, with applications to the Haar System in $L_{p} [0, 1]$ , $1 < p < \infty$

On Banach envelopes and duals of Lipschitz-free $p$ -spaces for $0 < p < 1$

Lipschitz free $p$ -spaces for $0 < p < 1$ in the light of the Schur $p$ -property and the compact reduction

Isomorphisms between vector-valued $H_{p}$ -spaces for $0 < p \leq 1$ and uniqueness of unconditional structure

Democracy of quasi-greedy bases in $p$ -Banach spaces with applications to the efficiency of the TGA in the Hardy spaces $H_{p} (D^{d})$