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Azagra Rueda, Daniel ; Gómez Gil, Javier ; Fry, Robb ; Lovo, Mauricio ; Jaramillo Aguado, Jesús Ángel | Oxford University Press | 2005-03We show that if X is a Banach space having an unconditional basis and a Cp-smooth Lipschitz bump function, then for every C1-smooth function f from X into a Banach space Y, and for every continuous function ? : X ? (0, ?), there exists a Cp-smoo[...]texto impreso
The authors survey some recent results concerning the question when the equality HomA=E holds for a subalgebra A of the algebra C(E) of continuous real-valued functions on a real Banach space E. A new natural proof for this equality is given in [...]texto impreso
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Let E and F be two real Banach spaces. For n = 0, 1, ...,1, let Cnw ub(E; F) be the space of n-times continuously differentiable functions f: E ! F such that, for each integer j _ n and each x 2 E, both the jth derivative mapping fj : E ! P(jE; [...]texto impreso
Garrido, M. Isabel ; Gómez Gil, Javier ; Jaramillo Aguado, Jesús Ángel | Universidad de Extremadura, Departamento de Matemáticas | 1992For an algebra A of continuous real-valued functions on a topological space X, the question of whether every algebra homomorphism is a point evaluation for a point in X is considered. A variety of results are provided, such as the following. Let[...]texto impreso
Garrido, M. Isabel ; Gómez Gil, Javier ; Jaramillo Aguado, Jesús Ángel | Canadian Mathematical Society | 1994Let A be an algebra of continuous real functions on a topological space X. We study when every nonzero algebra homomorphism phi:A --> R is given by evaluation at some point of X. In the case that A is the algebra of rational functions (or real-[...]texto impreso
Let (a(n)) be a weakly null Schauder basis of a Banach space E, and let (lambda(n)) be a convergent sequence of real numbers. We study the problem of finding an m-times weakly uniformly differentiable function f on E such that f(a(n)) = lambda(n[...]texto impreso
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We prove that every function f:Rn?R satisfies that the image of the set of critical points at which the function f has Taylor expansions of order n?1 and non-empty subdifferentials of order n is a Lebesgue-null set. As a by-product of our proof,[...]texto impreso
Let E and F be two Banach spaces and let A be a nonempty subset of E . A mapping f:A?F is said to be weakly continuous if it is continuous when A has the relative weak topology and F has the topology of its norm. Let A={E} , B= {A?E:A is[...]texto impreso
This paper is devoted to the question "Under what conditions on a Banach space E is it true that the bounded weak topology is locally convex?". The theorem of Banach and Dieudonné shows that reflexivity is a sufficient condition. The author prov[...]texto impreso
A characterization of dense polynomial algebras is obtained for a certain class of p-continously differentiable Fréchet functions between real Banach spaces. In order to study this result a new approximation property in Banach spaces, the bounde[...]texto impreso
In 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« . T[...]texto impreso
In this paper we solve the problem of extending continuous functions with nonempty subdifferential at every point of a closed subset A of R-n to functions with the same property defined in the whole Rn, keeping the property of outer semicontinui[...]
