# Compact and weakly compact homomorphisms between algebras of differentiable functions.

Manuel González; Joaquín M. Gutiérrez

Extracta Mathematicae (1990)

- Volume: 5, Issue: 3, page 118-120
- ISSN: 0213-8743

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topGonzález, Manuel, and Gutiérrez, Joaquín M.. "Compact and weakly compact homomorphisms between algebras of differentiable functions.." Extracta Mathematicae 5.3 (1990): 118-120. <http://eudml.org/doc/39886>.

@article{González1990,

abstract = {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.},

author = {González, Manuel, Gutiérrez, Joaquín M.},

journal = {Extracta Mathematicae},

keywords = {Espacios de funciones diferenciables; Funciones reales; Homomorfismos; weakly compact homomorphisms; algebras of differentiable functions},

language = {eng},

number = {3},

pages = {118-120},

title = {Compact and weakly compact homomorphisms between algebras of differentiable functions.},

url = {http://eudml.org/doc/39886},

volume = {5},

year = {1990},

}

TY - JOUR

AU - González, Manuel

AU - Gutiérrez, Joaquín M.

TI - Compact and weakly compact homomorphisms between algebras of differentiable functions.

JO - Extracta Mathematicae

PY - 1990

VL - 5

IS - 3

SP - 118

EP - 120

AB - 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.

LA - eng

KW - Espacios de funciones diferenciables; Funciones reales; Homomorfismos; weakly compact homomorphisms; algebras of differentiable functions

UR - http://eudml.org/doc/39886

ER -

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