Francisco Lisón Hernandez - Academia.edu (original) (raw)

Papers by Francisco Lisón Hernandez

Revista Matemática Iberoamericana

We study the structure of strictly singular non-compact operators between L p spaces. Answering a... more We study the structure of strictly singular non-compact operators between L p spaces. Answering a question raised in [17], it is shown that there exist operators T , for which the set of points (1 p , 1 q) ∈ (0, 1) × (0, 1) such that T : L p → L q is strictly singular but not compact contains a line segment in the triangle {(1 p , 1 q) : 1 < p < q < ∞} of any positive slope. This will be achieved by means of Riesz potential operators between metric measure spaces with different Hausdorff dimension. The relation between compactness and strict singularity of regular operators defined on subspaces of L p is also explored. i p,q : ℓ p ֒→ ℓ q 2010 Mathematics Subject Classification. 47B07, 46E30, 28A78.

La matematica educativa como disciplina cientifica ha recorrido un largo camino y ha librado nume... more La matematica educativa como disciplina cientifica ha recorrido un largo camino y ha librado numerosas batallas tratando de legitimizar su actividad en torno a la problematica que surge al observar con ojos cientificos los procesos de ensenanza y aprendizaje de las matematicas. En la Universidad Autonoma de Ciudad Juarez se ha gestado desde hace aproximadamente 15 anos un grupo de Matematica Educativa el cual ha contribuido a describir y caracterizar algunos aspectos en torno a dicha problematica, particularmente respecto al calculo En nuestra actividad como docentes nos hemos preocupado por identificar que es lo que los alumnos conocen o conceptualizan como derivada. Con este objetivo en mente se ha desarrollado un proyecto que trata de fortalecer el concepto de la primera derivada de una funcion valiendonos de actividades disenadas en Derive 6. El presente articulo da cuenta del desarrollo y evolucion que siguio este proyecto y algunos de los resultados que se obtuvieron, asi como...

Proceedings of the American Mathematical Society, 2000

We prove that each positive operator from a Banach lattice E to a Banach lattice F with a disjoin... more We prove that each positive operator from a Banach lattice E to a Banach lattice F with a disjointly strictly singular majorant is itself disjointly strictly singular provided the norm on F is order continuous. We prove as well that if S : E → E is dominated by a disjointly strictly singular operator, then S 2 is disjointly strictly singular.

Trends in Mathematics, 2019

Dedicated to Ben de Pagter on the occasion of his 65 th birthday.

Indagationes Mathematicae, 2020

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Journal of Mathematical Analysis and Applications, 2016

Trends in Mathematics, 2016

This is a survey on disjointly homogeneous Banach lattices and their applicactions. Several struc... more This is a survey on disjointly homogeneous Banach lattices and their applicactions. Several structural properties of this class are analyzed. In addition we show how these spaces provide a natural framework for studying the compactness of powers of operators allowing for a unified treatment of well-known results.

Journal of Mathematical Analysis and Applications, May 15, 2012

It is shown that a separable variable exponent (or Nakano) function space L p(•) (Ω) has a lattic... more 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 ∈ R p(•) , the essential range set of the exponent function p(•). Consequently R p(•) 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 ∈ R p(•) .

Journal of Mathematical Analysis and Applications, 2015

Definition Let B denote the class of all Banach spaces and let L denote the class of all bounded ... more Definition Let B denote the class of all Banach spaces and let L denote the class of all bounded linear operators between Banach spaces. An operator ideal I is a "mapping" I : B × B −→ 2 L satisfying the following conditions: Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 5 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 5 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 5 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 6 / 24 Ideal norms Definition An ideal norm defined on an ideal I is a rule • I that assigns to every operator T ∈ I a non-negative number T I satisfying the following conditions: Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 6 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 6 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 6 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 6 / 24 An ideal norm is a norm. Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 6 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 6 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 7 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 7 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 7 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 7 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 7 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 7 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 13 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 13 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 18 / 24 Consequences Corollary Let E and F be Banach spaces, and {I p : p ∈ [a, b]} be a family of operator ideals such that I p (E , F) I q (E , F) if p < q with continuous inclusion. Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 19 / 24 Consequences Corollary Let E and F be Banach spaces, and {I p : p ∈ [a, b]} be a family of operator ideals such that I p (E , F) I q (E , F) if p < q with continuous inclusion. If E or F is a σ-reproducible Banach space and I b (E , F) is complete for an ideal norm, then the set I b (E , F) \ p<b I p (E , F) is spaceable. Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 19 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 22 / 24 Víctor M. Sánchez (U.C.M.) Genericity and small sets in analysis 2015 May 27th 23 / 24

A Panorama of Modern Operator Theory and Related Topics, 2012

The super strict singularity of inclusions between rearrangement invariant function spaces on [0,... more The super strict singularity of inclusions between rearrangement invariant function spaces on [0, 1] is studied. Estimates of the Bernstein widths 𝛾n of the inclusions L∞ are given. It is showed that if the inclusion is strong and the order continuous part of exp E2 is not included in ⊂ then the inclusion ?? F is super strictly singular. Applications to the classes of Lorentz and Orlicz spaces are given.

$Research paper thumbnail of On embeddings of function spaces into 𝐿^{𝑝}+𝐿^{𝑞}$

Contemporary Mathematics, 1993

Studia Mathematica, 2009

If G is the closure of L∞ in exp L2, it is proved that the inclusion between rearrangement invari... more If G is the closure of L∞ in exp L2, it is proved that the inclusion between rearrangement invariant spaces E ⊂ F is strictly singular if and only if it is disjointly strictly singular and E ⊃ G. For any Marcinkiewicz space M (ϕ) ⊂ G such that M (ϕ) is not an interpolation space between L∞ and G it is proved that there exists another Marcinkiewicz space M (ψ) M (ϕ) with the property that the M (ψ) and M (ϕ) norms are equivalent on the Rademacher subspace. Applications are given and a question of Milman answered.

The Quarterly Journal of Mathematics, 2007

It is proved that every positive operator R on a Banach lattice E dominated by a strictly singula... more It is proved that every positive operator R on a Banach lattice E dominated by a strictly singular operator T : E → E satisfies that the R 4 is strictly singular. Moreover, if E is order continuous then the R 2 is already strictly singular.

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2004

We study inclusion indices relative to an interpolation scale. Applications are given to several ... more We study inclusion indices relative to an interpolation scale. Applications are given to several families of functions spaces.

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1996

Interpolation properties of the class of disjointly strictly singular operators on Banach lattice... more 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.

Positivity, 2010

We survey recent results on domination properties of strictly singular operators and related oper... more We survey recent results on domination properties of strictly singular operators and related operator ideals, as well as Banach-Saks operators, Narrow operators and p-summing operators.

Journal of the London Mathematical Society, 2002

Page 1. J. London Math. Soc. (2) 66 (2002) 433452 Cf2002 London Mathematical Society DOI: 10.111... more Page 1. J. London Math. Soc. (2) 66 (2002) 433452 Cf2002 London Mathematical Society DOI: 10.1112/S0024610702003447 DOMINATION BY POSITIVE STRICTLY SINGULAR OPERATORS JULIO FLORES and FRANCISCO L. HERN ´ANDEZ 1. Introduction ...

Journal of the London Mathematical Society, 2009

Journal of Functional Analysis, 2014

We study several properties of disjointly homogeneous Banach lattices with a special focus on two... more We study several properties of disjointly homogeneous Banach lattices with a special focus on two questions: the self-duality of this class and the existence of disjoint sequences spanning complemented subspaces. Positive results concerning these problems are provided. Moreover, we give examples of reflexive disjointly homogenous spaces whose dual spaces are not, answering the first question in the negative.