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This paper is a survey of approximation results and methods by smooth functions in Banach spaces. The topics considered in the paper are the following: approximation by polynomials by C-k-functions using the method of smooth partitions of unity,[...]texto impreso
This self-contained book brings together the important results of a rapidly growing area.As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells' theorem and Aron's theorem for t[...]texto impreso
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In this note we study the relationship between compactness and weak compactness of a continuous homomorphism A from Cco(S) into Cco(T) and the associated continuous function ' : T ! S, where S and T are completely regular Hausdorff spaces.texto impreso
Let E and F be Banach spaces and let Cwu(E) be the Fréchet algebra of real-valued functions on E which are uniformly weakly continuous when restricted to any bounded subset of E. Homomorphisms, and properties of such homomorphisms, between Cwu(E[...]texto impreso
Let E, F be real Banach spaces, U subset-or-equal-to E and V subset-equal-to F non-void open subsets and C(k)(U) the algebra of real-valued k-times continuously Frechet differentiable functions on U, endowed with the compact open topology of ord[...]texto impreso
A characterization of uniform continuity for maps between unit balls of real Banach spaces is given in terms of universal properties. Also, it is shown that the classes of compact and weakly compact composition operators induced by such maps agree.texto impreso
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Consider the following possible properties which a Banach space X may have: (P): If (x(j)) and (y(j)) are are bounded sequences in X such that for all n greater than or equal to 1 and for every continuous n-homogeneous polynomial P on X, P(x(j))[...]texto impreso
The main result in this paper is a representation theorem for homogeneous orthogonally additive polynomials on Banach lattices. The representation theorem is used to study the linear span of the set of zeros of homogeneous real-valued orthogonal[...]texto impreso
We begin this paper with a general study of algebra homomorphisms between algebras of continuous real functions on completely regular topological spaces; we study their automatic continuity and we characterize them as induced by continuous maps;[...]texto impreso
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; [...]
