Person: Jaramillo Aguado, Jesús Ángel
Universidad Complutense de Madrid
Faculty / Institute
Análisis Matemático Matemática Aplicada
Now showing 1 - 10 of 66
PublicationSmoothness and Estimates of Sequences in Banach-Spaces(Magnes Press, 1995) Gonzalo, R.; Jaramillo Aguado, Jesús ÁngelAn upper bound for the order of smoothness of bump functions in Banach spaces without copy of c(0) is found in terms of lower and upper estimates of their sequences. It is also shown that every C-infinity-smooth Banach space with symmetric basis either contains c(0) or is isomorphic to l(2n) for some integer n. PublicationRolle’s Theorem and Negligibility of Points in Infinite Dimensional Banach Spaces(Elsevier, 1997-09-15) Azagra Rueda, Daniel; Gómez Gil, Javier; Jaramillo Aguado, Jesús ÁngelIn this note we prove that if a differentiable function oscillates between y« and « on the boundary of the unit ball then there exists a point in the interior of the ball in which the differential of the function has norm equal or less than« . This kind of approximate Rolle’s theorem is interesting because an exact Rolle’s theorem does not hold in many infinite dimensional Banach spaces. A characterization of those spaces in which Rolle’s theorem does not hold is given within a large class of Banach spaces. This question is closely related to the existence of C1 diffeomorphisms between a Banach space X and X _ _04 which are the identity out of a ball, and we prove that such diffeomorphisms exist for every C1 smooth Banach space which can be linearly injected into a Banach space whose dual norm is locally uniformly rotund (LUR). PublicationExtension of bilinear forms on Banach spaces(American Mathematical Society, 2001) Castillo, Jesús M.F.; García, R.; Jaramillo Aguado, Jesús ÁngelWe study the extension of bilinear and multilinear forms from a given subspace of a Banach space to the whole space. Precisely, an isomorphic embedding j : E --> X is said to be (linearly) N-exact if N-linear forms on E can be (linear and continuously) extended to X through j. We present some necessary and sufficient conditions for j to be 2-exact, as well as several examples of 2-exact embeddings. We answer a problem of Zalduendo: in a cotype 2 space bilinear extendable and integral forms coincide. PublicationRemarks on the weak-polynomial convergence on a Banach space(Universidad de Extramadura, Departamento de Matemáticas, 1991) Jaramillo Aguado, Jesús Ángel; Prieto Yerro, M. ÁngelesWe shall be concerned in this note with some questions posed by Carne, Cole and Gamelin in , involving the weak-polynomial convergence and its relation to the tightness of certain algebras of analytic functions on a Banach space PublicationGlobal inversion of nonsmooth mappings on Finsler manifolds(Heldermann Verlag, 2013) Jaramillo Aguado, Jesús Ángel; Madiedo, Oscar; Sánchez González, LuisWe consider the problem of finding sufficient conditions for a locally Lipschitz mapping between Finsler manifolds to be a global homeomorphism. For this purpose, we develop the notion of Clarke generalized differential in this context and, using this, we obtain a version of the Hadamard integral condition for invertibility. As consequences, we deduce some global inversion and global injectivity results for Lipschitz mappings on R-n in terms of spectral conditions of its Clarke generalized differential. PublicationHomomorphisms on function lattices(Springer, 2004) Garrido, M. Isabel; Jaramillo Aguado, Jesús ÁngelIn this paper we study real lattice homomorphisms on a unital vector lattice L subset of C(X), where X is a completely regular space. We stress on topological properties of its structure spaces and on its representation as point evaluations. These results are applied to the lattice L = Lip(X) of real Lipschitz functions on a metric space. Using the automatic continuity of lattice homomorphisms with respect to the Lipschitz norm, we are able to derive a Banach-Stone theorem in this context. Namely, it is proved that the unital vector lattice structure of Lip (X) characterizes the Lipschitz structure of the complete metric space X. In the case L = Lip (X) of bounded Lipschitz functions, an analogous result is obtained in the class of complete quasiconvex metric spaces. PublicationAn Example on Composite Differentiable Functions in Infinite Dimensions(Australian Mathematics Publ Assoc Inc, 1989-08) Jaramillo Aguado, Jesús ÁngelWe present an example showing that a classical result due to Glaeser about the closedness of composition subalgebras of infinitely differeuniable functions cannot be extended to the case of weakly uniformly differentiable functions on Banach spaces PublicationTopologies and homomorphisms on algebras of differentiable functions(Japanese Association of mathematical Sciences, 1990-03) Jaramillo Aguado, Jesús Ángel PublicationLinearization and compactness(Polish Acad Sciences Inst Mathematics, 2009) Jaramillo Aguado, Jesús Ángel; Prieto Yerro, M. Ángeles; Zalduendo, IgnacioThis paper is devoted to several questions concerning linearizations of function spaces. We first consider the relation between linearizations of a given space when it is viewed as a function space over different domains. Then we study the problem of characterizing when a Banach function space admits a Banach linearization in a natural way. Finally, we consider the relevance of compactness properties in linearizations, more precisely, the relation between different compactness properties of a mapping, and compactness of its associated linear operator. PublicationDuality and reflexivity in spaces of polynomials(Birkhauser Verlag, 2000-04) Jaramillo Aguado, Jesús Ángel; Moraes, L.A.We first study the reflexivity of the space P(E-m,F) of continuous m-homogeneous polynomials between Banach spaces E and F. Then, in a more general way, we obtain conditions under which the spaces P(E-m,F)(n) and P(E-m",F") are canonically isomorphic.