Polynomial continuity (Russian)

The First International School "Functional Analysis, Differential Equations and Their Application" Puebla (Mexico), May 18--23, 1995Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu

Representation of non-semibounded quadratic forms and orthogonal additivity

In this article we give a representation theorem for non-semibounded Hermitean quadratic forms in terms of a (non-semibounded) self-adjoint operator. The main assumptions are closability of the Hermitean quadratic form, the direct integral structure of the underlying Hilbert space and orthogonal additivity. We apply this result to several examples, including the position operator in quantum mechanics and quadratic forms invariant under a unitary representation of a separable locally compact group. The case of invariance under a compact group is also discussed in detail

The approximation property in spaces of differentiable functions. (Spanish: La propiedad de aproximación en espacios de funciones diferenciables).

Let E and X be real Banach and locally convex spaces, respectively. Let Ccn(E,X) denote the space of n times continuously Hadamard differentiable functions f:E→X, endowed with the locally convex topology generated by the seminorms of the form f∈Ccn(E,X)→sup{α[Dpf(x)(y)]:x,y∈K}, where p∈N, p≤n, K⊂E is compact, and α is a continuous seminorm on X. The authors show that Ccn(E,X) is complete if X is complete, and investigate the relationship between approximation in Ccn(E,X) and the approximation property of E. For example, if X is complete, then Ccn(E,X) is topologically isomorphic to the ε-product of Ccn(E,R) and X. Using this result, the authors show that the following properties are equivalent: (a) E has the approximation property, (b) Ccn(E,R) has the approximation property for all (equivalently, for some) n≥1, and (c) for all X, Ccn(E,R)⊗X is dense in Ccn(E,X) for all (equivalently, for some) n≥1. Similar questions have been considered for the space Cn(E,X) of n times continuously Fréchet differentiable functions, endowed with the same locally convex topology. For example, the equivalence of (a) and (b) was proved by the first author (""Differentiable functions with the approximation property'', to appear) and the reviewer [Infinite dimensional holomorphy and applications (Proc. Internat. Sympos., Campinas, 1975), pp. 1–17, North-Holland, Amsterdam, 1977; see also Séminaire Pierre Lelong (Analyse), Année 1974/75, pp. 213–222, Lecture Notes in Math., Vol. 524, Springer, Berlin, 1976. It is apparently unknown whether Cn(E,R) is complete with this topology. Results relating the approximation property of E to approximation of Fréchet differentiable functions defined on open subsets of E and to generalized differentiable versions of the Stone-Weierstrass theorem have been obtained by J. B. Prolla and C. S. Guerreiro [Ark. Mat. 14 (1976), no. 2, 251–258]

Multiplicatively functionals on function álgebras

Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUECAICYTpu

Polynomials and geometry of Banach space

In this paper we survey a large part of the results on polynomials on Banach spaces that have been obtained in recent years. We mainly look at how the polynomials behave in connection with certain geometric properties of the spaces

RICORS2040 : The need for collaborative research in chronic kidney disease

Chronic kidney disease (CKD) is a silent and poorly known killer. The current concept of CKD is relatively young and uptake by the public, physicians and health authorities is not widespread. Physicians still confuse CKD with chronic kidney insufficiency or failure. For the wider public and health authorities, CKD evokes kidney replacement therapy (KRT). In Spain, the prevalence of KRT is 0.13%. Thus health authorities may consider CKD a non-issue: very few persons eventually need KRT and, for those in whom kidneys fail, the problem is 'solved' by dialysis or kidney transplantation. However, KRT is the tip of the iceberg in the burden of CKD. The main burden of CKD is accelerated ageing and premature death. The cut-off points for kidney function and kidney damage indexes that define CKD also mark an increased risk for all-cause premature death. CKD is the most prevalent risk factor for lethal coronavirus disease 2019 (COVID-19) and the factor that most increases the risk of death in COVID-19, after old age. Men and women undergoing KRT still have an annual mortality that is 10- to 100-fold higher than similar-age peers, and life expectancy is shortened by ~40 years for young persons on dialysis and by 15 years for young persons with a functioning kidney graft. CKD is expected to become the fifth greatest global cause of death by 2040 and the second greatest cause of death in Spain before the end of the century, a time when one in four Spaniards will have CKD. However, by 2022, CKD will become the only top-15 global predicted cause of death that is not supported by a dedicated well-funded Centres for Biomedical Research (CIBER) network structure in Spain. Realizing the underestimation of the CKD burden of disease by health authorities, the Decade of the Kidney initiative for 2020-2030 was launched by the American Association of Kidney Patients and the European Kidney Health Alliance. Leading Spanish kidney researchers grouped in the kidney collaborative research network Red de Investigación Renal have now applied for the Redes de Investigación Cooperativa Orientadas a Resultados en Salud (RICORS) call for collaborative research in Spain with the support of the Spanish Society of Nephrology, Federación Nacional de Asociaciones para la Lucha Contra las Enfermedades del Riñón and ONT: RICORS2040 aims to prevent the dire predictions for the global 2040 burden of CKD from becoming true

Approximation by ck-functions - Preliminary report

Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu

Approximation of differentiable functions

Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu

Weak topologies on bounded sets of a Banach space. Associated function spaces.

This is a survey paper concerning:\par 1) relations between spaces of weakly continuous functions on Banach spaces and their weak topologies;\par 2) weakly continuous and weakly differentiable function spaces in relation with the extension of Weierstrass' theorem for infinite dimensional Banach spaces;\par 3) interpolation of bounded sequences by weakly continuous and weakly differentiable functions

Polynomial continuity on Banach spaces

5th International Conference on Function Spaces. 1998. POZNAN, POLAND.Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu