Compact and weakly compact homomorphisms between algebras of differentiable functions.

Título inglés	Compact and weakly compact homomorphisms between algebras of differentiable functions.
Título español	Homomorfismos compactos y débilmente compactos entre álgebras de funciones diferenciables.
Autor/es	González, Manuel ; Gutiérrez, Joaquín M.
Organización	Dep. Mat. Fac. Cienc. Univ. Cantabria, Santander, España;Dep. Mat. Esc. Téc. Sup. Ingen. Industr. Univ. Politéc. Madrid, Madrid, España
Revista	0213-8743
Publicación	1990, 5 (3): 118-120, 3 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	Many authors have recently studied compact and weakly compact homomorphisms between function algebras. Among them, Lindström and Llavona [2] treat weakly compact continuous homomorphisms between algebras of type C(T) when T is a completely regular Hausdorff space. Llavona asked wether the results in [2] are valid in the case of algebras of differentiable functions on Banach spaces. The purpose of this note is to give an affirmative answer to this question, by proving that weakly compact homomorphisms between algebras of differentiable functions are induced by constant mappings. The difficulty we face is that in [2] the existence of continuous functions separating points and closed sets plays an essential role, while in the differentiable case these functions do not exist in general. We deal with Fréchet differentiability, but our results are also valid for Hadamard differentiable functions.
Clasificación UNESCO	120203
Palabras clave español	Espacios de funciones diferenciables ; Funciones reales ; Homomorfismos
Código MathReviews	MR1125678
Código Z-Math	Zbl 0743.46019
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