Albiac Alesanco, Fernando José

Profile Picture

Email Address

person.page.identifierURI

https://academica-e.unavarra.es/handle/2454/48472

Birth Date

Job Title

Last Name

Albiac Alesanco

First Name

Fernando José

person.page.departamento

Estadística, Informática y Matemáticas

person.page.instituteName

InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

ORCID

0000-0001-7051-9279

person.page.observainves

88452

person.page.upna

504

Name

Filters

2022 - 20233
Reset filters

Settings

Author: Ansorena, José L. × Subject: Hardy spaces ×

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    PublicationOpen Access
    Uniqueness of unconditional basis of ℓ2⊕T(2)
    (American Mathematical Society, 2022) Albiac Alesanco, Fernando José; Ansorena, José L.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    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 bases of their summands. The general splitting principle we obtain yields, in particular, that if each Xi has a unique unconditional basis (up to equivalence and permutation), then X1 · · · Xn has a unique unconditional basis too. Among the novel applications of our techniques to the structure of Banach and quasi-Banach spaces we have that the space ℓ2⊕T(2) has a unique unconditional basis.
  • Thumbnail Image
    PublicationOpen Access
    Uniqueness of unconditional basis of Hp(T) ⊕ 2 and Hp(T) ⊕ T (2) for 0 < p < 1
    (Elsevier, 2022) Albiac Alesanco, Fernando José; Ansorena, José L.; Wojtaszczyk, Przemyslaw; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
    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 space Y which guarantee that every unconditional basis of their direct sum X ⊕ Y splits into unconditional bases of each summand. As application of our methods we obtain that, among others, the spaces Hp(Td) ⊕ T (2) and Hp(Td) ⊕ 2, for p ∈ (0, 1) and d ∈ N, have a unique unconditional basis (up to equivalence and permutation).
  • Thumbnail Image
    PublicationOpen Access
    Democracy of quasi-greedy bases in p-Banach spaces with applications to the efficiency of the thresholding greedy algorithm in the hardy spaces Hp(Dd)
    (Cambridge University Press, 2023) Albiac Alesanco, Fernando José; Ansorena, José L.; Bello, Glenier; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
    We use new methods, specific for non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a -Banach space for 0 < p < p are democratic. The novel techniques we obtain permit to show in particular that all quasi-greedy bases of the Hardy Hp(D) space for 0 < p < 1 are democratic while, in contrast, no quasi-greedy basis of Hp(Dd) for d > 2 is, solving thus a problem that was raised in [7]. Applications of our results to other spaces of interest both in functional analysis and approximation theory are also provided.