Browsing by Author "Ansorena, José L."

Now showing items 1-20 of 22

    • Addendum to "uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces" 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L. (Springer, 2022)   Artículo / Artikulua  OpenAccess
      After [Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces, Positivity 26 (2022), Paper no. 35] was published, we realized that Theorem 4.2 therein, when combined with work of Casazza and Kalton ...

    • Asymptotic greediness of the Haar system in the spaces Lp[0 , 1] , 1< p< ∞ 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Berná, Pablo M. (Springer, 2019)   Artículo / Artikulua  OpenAccess
      Our aim in this paper is to attain a sharp asymptotic estimate for the greedy constant Cg[H(p), Lp] of the (normalized) Haar system H(p) in Lp[0 , 1] for 1 < p < ∞. We will show that the super-democracy constant of H(p) ...

    • Bidemocratic bases and their connections with other greedy-type bases 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Berasategui, Miguel; Berná, Pablo M.; Lassalle, Silvia (Springer, 2023)   Artículo / Artikulua  OpenAccess
      In nonlinear greedy approximation theory, bidemocratic bases have traditionally played the role of dualizing democratic, greedy, quasi-greedy, or almost greedy bases. In this article we shift the viewpoint and study them ...

    • Building highly conditional almost greedy and quasi-greedy bases in Banach spaces 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Dilworth, S. J.; Kutzarova, Denka (Elsevier, 2019)   Artículo / Artikulua  OpenAccess
      It is known that for a conditional quasi-greedy basis B in a Banach space X, the associated sequence (k(m)[B](m=1)(infinity) of its conditionality constants verifies the estimate k(m)[B] = O(log m) and that if the reverse ...

    • Conditional quasi-greedy bases in non-superreflexive Banach spaces 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Wojtaszczyk, Przemyslaw (Springer, 2019)   Artículo / Artikulua  OpenAccess
      For a conditional quasi-greedy basis B in a Banach space, the associated conditionality constants km[B] verify the estimate km[B]=O(logm). Answering a question raised by Temlyakov, Yang, and Ye, several authors have studied ...

    • Embeddability of ℓp and bases in Lipschitz free p-spaces for 0 < p ≤ 1 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Cúth, Marek; Doucha, Michal (Elsevier, 2020)   Artículo / Artikulua  OpenAccess
      Our goal in this paper is to continue the study initiated by the authors in of the geometry of the Lipschitz free p-spaces over quasimetric spaces for 0 < p ≤ 1, denoted Fp(M). Here we develop new techniques to show that, ...

    • Greedy approximation for biorthogonal systems in quasi-Banach spaces 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Berná, Pablo M.; Wojtaszczyk, Przemyslaw (Instytut Matematyczny, 2021)   Artículo / Artikulua  OpenAccess
      The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems in quasi-Banach spaces from a functional-analytic point of view. If ...

    • Lipschitz algebras and Lipschitz-Free spaces over unbounded metric spaces 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Cúth, Marek; Doucha, Michal (Oxford University Press, 2021)   Artículo / Artikulua  OpenAccess
      We investigate a way to turn an arbitrary (usually, unbounded) metric space M into a bounded metric space B in such a way that the corresponding Lipschitz-free spaces F(M) and F(B) are isomorphic. The construction we provide ...

    • Lipschitz free p-spaces for 0 < p < 1 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Cúth, Marek; Doucha, Michal (SpringerHebrew University Magnes Press, 2020)   Artículo / Artikulua  OpenAccess
      This paper initiates the study of the structure of a new class of p-Banach spaces, 0 <p < 1, namely the Lipschitz free p-spaces (alternatively called Arens—Eells p-spaces) Fp(M) over p-metric spaces. We systematically ...

    • Lipschitz free spaces isomorphic to their infinite sums and geometric applications 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Cúth, Marek; Doucha, Michal (American Mathematical Society, 2021)   Artículo / Artikulua  OpenAccess
      We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct _1-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free ...

    • New parameters and Lebesgue-type estimates in greedy approximation 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Berná, Pablo M. (Cambridge University Press, 2022)   Artículo / Artikulua  OpenAccess
      The purpose of this paper is to quantify the size of the Lebesgue constants (𝑳𝑚)∞ 𝑚=1 associated with the thresholding greedy algorithm in terms of a new generation of parameters that modulate accurately some features ...

    • Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Dilworth, S. J.; Kutzarova, Denka (Instytut Matematyczny, 2020)   Artículo / Artikulua  OpenAccess
      We settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non-superreflexive mixed-norm sequence space. As a by-product, ...

    • On a 'philosophical' question about Banach envelopes 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Wojtaszczyk, Przemyslaw (Springer, 2021)   Artículo / Artikulua  OpenAccess
      We show how to construct non-locally convex quasi-Banach spaces X whose dual separates the points of a dense subspace of X but does not separate the points of X. Our examples connect with a question raised by Pietsch (Rev ...

    • On certain subspaces of p for 0 < p ≤ 1 and their applications to conditional quasi-greedy bases in p-Banach spaces 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Wojtaszczyk, Przemyslaw (Springer, 2021)   Artículo / Artikulua  OpenAccess
      We construct for each 0<p≤1 an infinite collection of subspaces of ℓp that extend the example of Lindenstrauss (Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12, 539–542, 1964) of a subspace of ℓ1 with no ...

    • On the permutative equivalence of squares of unconditional bases 

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L. (Elsevier, 2022)   Artículo / Artikulua  OpenAccess
      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 Upna Orcid; Ansorena, José L. (Wiley, 2021)   Artículo / Artikulua  OpenAccess
      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 Upna Orcid; Ansorena, José L.; Wojtaszczyk, Przemyslaw (Elsevier, 2020)   Artículo / Artikulua  OpenAccess
      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. ...

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

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Cúth, Marek; Doucha, Michal (Springer, 2021)   Artículo / Artikulua  OpenAccess
      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, ...

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

      Albiac Alesanco, Fernando José Upna Orcid; Ansorena, José L.; Ciaurri, Óscar; Varona, Juan L. (European Mathematical Society, 2019)   Artículo / Artikulua  OpenAccess
      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 Upna Orcid; Ansorena, José L.; Wojtaszczyk, Przemyslaw (Elsevier, 2022)   Artículo / Artikulua  OpenAccess
      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 ...

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