Listar Artículos de revista - Aldizkari artikuluak por autor UPNA "Albiac Alesanco, Fernando José"

On the permutative equivalence of squares of unconditional bases

Albiac Alesanco, Fernando José

; Ansorena, José L. (Elsevier, 2022) Artículo / Artikulua

We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty-five year-old question raised by Casazza and Kalton ...

Projections and unconditional bases in direct sums of ℓp SPACES, 0<p≤∞

Albiac Alesanco, Fernando José

; Ansorena, José L. (Wiley, 2021) Artículo / Artikulua

We show that every unconditional basis in a finite direct sum ⊕p∈Aℓp , with A ⊂ (0,∞], splits into unconditional bases of each summand. This settles a 40 years old question raised in 'A. Ortyński, Unconditional bases in ...

Quasi-greedy bases in ℓp (0 < p < 1) are democratic

Albiac Alesanco, Fernando José

; Ansorena, José L.; Wojtaszczyk, Przemyslaw (Elsevier, 2020) Artículo / Artikulua

The list of known Banach spaces whose linear geometry determines the (nonlinear) democracy functions of their quasi-greedy bases to the extent that they end up being democratic, reduces to c0, ℓ2, and all separable L1-spaces. ...

Sparse approximation using new greedy-like bases in superreflexive spaces

Albiac Alesanco, Fernando José

; Ansorena, José L.; Berasategui, Miguel (Instytut Matematyczny, 2023) Artículo / Artikulua

This paper is devoted to theoretical aspects of optimality of sparse approximation. We undertake a quantitative study of new types of greedy-like bases that have recently arisen in the context of non-linear m-term approximation ...

Structure of the Lipschitz free p-spaces Fp(Zd) and Fp(Rd) for 0 < p ≤ 1

Albiac Alesanco, Fernando José

; Ansorena, José L.; Cúth, Marek; Doucha, Michal (Springer, 2021) Artículo / Artikulua

Our aim in this article is to contribute to the theory of Lipschitz free p-spaces for 0 < p ≤ 1 over the Euclidean spaces Rd and Zd. To that end, on one hand we show that Fp(Rd) admits a Schauder basis for every p ∈ 2 (0, ...

Submultiplicative norms in CC(K) spaces with applications to uniform algebras

Albiac Alesanco, Fernando José

; Blasco, Óscar; Briem, E. (Springer, 2024) Artículo / Artikulua

Certain algebra norms on the algebra of functions on a two-point set are defined and used to construct a new family of parametric algebra norms on the space CC(K) of continuous complex-valued functions on a compact Hausdorff ...

The Tsirelson space tau (p) has a unique unconditional basis up to permutation for 0 < p < 1

Albiac Alesanco, Fernando José

; Leránoz Istúriz, María Camino

(Hindawi Publishing Corporation, 2009) Artículo / Artikulua

We show that the p-convexified Tsirelson space tau((p)) for 0 < p < 1 and all its complemented subspaces with unconditional basis have unique unconditional basis up to permutation. The techniques involved in the proof are ...

Unconditional and quasi-greedy bases in L-p with applications to Jacobi polynomials Fourier series

Albiac Alesanco, Fernando José

; Ansorena, José L.; Ciaurri, Óscar; Varona, Juan L. (European Mathematical Society, 2019) Artículo / Artikulua

We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in L-p does not converge unless p = 2. As a by-product of our work on quasi-greedy bases in L-p(µ), we ...

Uniqueness of unconditional basis of Hp(T) ⊕ 2 and Hp(T) ⊕ T (2) for 0 < p < 1

Albiac Alesanco, Fernando José

; Ansorena, José L.; Wojtaszczyk, Przemyslaw (Elsevier, 2022) Artículo / Artikulua

Our goal in this paper is to advance the state of the art of the topic of uniqueness of unconditional basis. To that end we establish general conditions on a pair (X, Y) formed by a quasi-Banach space X and a Banach ...

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

Albiac Alesanco, Fernando José

; Ansorena, José L. (Kluwer Academic Publishers, 2022) Artículo / Artikulua

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-Banach spaces. Our new approach to this type ...

Uniqueness of unconditional basis of ℓ2⊕T(2)

Albiac Alesanco, Fernando José

; Ansorena, José L. (American Mathematical Society, 2022) Artículo / Artikulua

We provide a new extension of Pitt’s theorem for compact operators between quasi-Banach lattices which permits to describe unconditional bases of finite direct sums of Banach spaces X1 · · · Xn as direct sums of unconditional ...

Weak forms of unconditionality of bases in greedy approximation

Albiac Alesanco, Fernando José

; Ansorena, José L.; Berasategui, Miguel; Berná, Pablo M.; Lassalle, Silvia (Instytut Matematyczny, 2022) Artículo / Artikulua

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 greedy algorithm. We measure how far these bases are ...