Ruiz Bermejo, César

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First Name
Last Name
Ruiz Bermejo
Universidad Complutense de Madrid
Faculty / Institute
Análisis Matemático Matemática Aplicada
Análisis Matemático
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Now showing 1 - 9 of 9
  • Publication
    Averaging and orthogonal operators on variable exponent spaces L-p(.) (Omega)
    (Elsevier, 2014-05) Hernández, Francisco L.; Ruiz Bermejo, César
    Given a measurable space (Omega, mu) and a sequence of disjoint measurable subsets A = (A(n))(n), the associated averaging projection P-A and the orthogonal projection T-A are considered. We study the boundedness of these operators on variable exponent spaces L-P(.) (Omega). These operators are unbounded in general. Sufficient conditions on the sequence A in order to achieve that P-A or T-A be bounded are given. Conditions which provide the boundedness of P-A imply that T-A is also bounded. The converse is not true. Some applications are given. In particular, we obtain a sufficient condition for the boundedness of the Hardy-Littlewood maximal operator on spaces L-P(.) (Omega).
  • Publication
    Spaceability and operator ideals
    (Elsevier, 2015-11) Hernández, Francisco L.; Ruiz Bermejo, César; Sánchez de los Reyes, Víctor Manuel
    Let I1 and I2 be arbitrary operator ideals in the sense of Pietsch and E and F be Banach spaces such that the set I1(E,F){set minus}I2(E,F) is non-empty. We give a quite general sufficient condition on the Banach spaces in order to obtain the spaceability of I1(E,F){set minus}I2(E,F). Some consequences are provided when considering the ideals of compact operators, strictly singular operators, finitely strictly singular operators and Schatten operator classes.
  • Publication
    The convex hull of a Banach-Saks set
    (Elsevier, 2014) López Abad, J.; Ruiz Bermejo, César; Tradacete Pérez, Pedro
    A subset A of a Banach space is called Banach–Saks when every sequence in A has a Cesàro convergent subsequence. Our interest here focuses on the following problem: is the convex hull of a Banach–Saks set again Banach–Saks? By means of a combinatorial argument, we show that in general the answer is negative. However, sufficient conditions are given in order to obtain a positive result.
  • Publication
    Weak compactness in variable exponent spaces
    (Elsevier, 2021) Hernández, Francisco L.; Ruiz Bermejo, César; Sanchiz, Mauro
    This paper shows necessary and sufficient conditions on subsets of variable exponent spaces Lp(·)(Ω) in order to be weakly compact. Useful criteria are given extending Andô results for Orlicz spaces. As application, we prove that all separable variable exponent spaces are weakly Banach-Saks. Also, L-weakly compact and weakly compact inclusions between variable exponent spaces are studied.
  • Publication
    Nonlinear subsets of function spaces and spaceability
    (Elsevier, 2014-12) Ruiz Bermejo, César; Sánchez de los Reyes, Víctor Manuel
    In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0,1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class such that the inclusion operator is disjointly strictly singular. We consider Lorentz, Marcinkiewicz and Orlicz spaces. The answer is affirmative for Marcinkiewicz spaces and negative for Lorentz and Orlicz spaces. Also, the same problem is studied for Nakano spaces assuming different hypothesis
  • Publication
    Weak compactness and representation in variable exponent Lebesgue spaces on infinite measure spaces
    (Springer Nature, 2022-07-16) Hernández, Francisco L.; Ruiz Bermejo, César; Sanchiz Alonso, Mauro
    Relative weakly compact sets and weak convergence in variable exponent Lebesgue spaces L p(·) () for infinite measure spaces (, μ) are characterized. Criteria recently obtained in [14] for finite measures are here extended to the infinite measure case. In particular, it is showed that the inclusions between variable exponent Lebesgue spaces for infinite measures are never L-weakly compact. A lattice isometric representation of L p(·) () as a variable exponent space Lq(·) (0, 1) is given.
  • Publication
    Subprojective Nakano spaces
    (Elsevier, 2018) Ruiz Bermejo, César; Sánchez de los Reyes, Víctor Manuel
    A Banach space X is subprojective if every infinite-dimensional subspace of X has a subspace which is complemented in X. We prove that separable Nakano sequence spaces l((pn)) are subprojective. Subprojectivity is also characterized in separable Nakano function spaces L-p(.) (0,1) and L-p(.) (0, infinity). (C).
  • Publication
    l(q)-structure of variable exponent spaces
    (Elsevier, 2012-05-15) Hernández, Francisco L.; Ruiz Bermejo, César
    It is shown that a separable variable exponent (or Nakano) function space L-p(.)(Ω) has a lattice-isomorphic copy of l(q) if and only if q is an element of Rp(.), the essential range set of the exponent function p(.). Consequently Rp(.) is a lattice-isomorphic invariant set. The values of q such that l(q) embeds isomorphically in L-p(.)(Ω) is determined. It is also proved the existence of a bounded orthogonal l(q)-projection in the space L-p(.)(Ω), for every q is an element of Rp(.)
  • Publication
    Disjointly strictly singular operators and interpolation
    (Cambridge University Press, 1996) García del Amo Jiménez, Alejandro José; Hernández, Francisco L.; Ruiz Bermejo, César
    Interpolation properties of the class of disjointly strictly singular operators on Banach lattices are studied. We also give some applications to compare the lattice structure of two rearrangement invariant function spaces. In particular, we obtain suitable analytic characterisations of when the inclusion map between two Orlicz function spaces is disjointly strictly singular.