# Homomorphisms on some function algebras.

M.ª Isabel Garrido; Javier Gómez Gil; Jesús Angel Jaramillo

Extracta Mathematicae (1992)

- Volume: 7, Issue: 1, page 46-52
- ISSN: 0213-8743

## Access Full Article

top## Abstract

top## How to cite

topGarrido, M.ª Isabel, Gómez Gil, Javier, and Jaramillo, Jesús Angel. "Homomorphisms on some function algebras.." Extracta Mathematicae 7.1 (1992): 46-52. <http://eudml.org/doc/39964>.

@article{Garrido1992,

abstract = {Suppose that A is an algebra of continuous real functions defined on a topological space X. We shall be concerned here with the problem as to whether every nonzero algebra homomorphism φ: A → R is given by evaluation at some point of X, in the sense that there exists some a in X such that φ(f) = f(a) for every f in A. The problem goes back to the work of Michael [19], motivated by the question of automatic continuity of homomorphisms in a symmetric *-algebra. More recently, the problem has been considered by several authors, mainly in the case of algebras of smooth functions: algebras of differentiable functions on a Banach space in [2], [11], [13] and [14]; algebras of differentiable functions on a locally convex space in [3], [4], [5] and [6], and algebras of smooth functions in the abstract context of smooth spaces in [18]. We shall be interested both in the general case and in the case of functions on a Banach space. This report is based on the results obtained in [8].},

author = {Garrido, M.ª Isabel, Gómez Gil, Javier, Jaramillo, Jesús Angel},

journal = {Extracta Mathematicae},

keywords = {Algebra de funciones; Homomorfismos; Anillos de funciones; Funcionales multiplicativos},

language = {eng},

number = {1},

pages = {46-52},

title = {Homomorphisms on some function algebras.},

url = {http://eudml.org/doc/39964},

volume = {7},

year = {1992},

}

TY - JOUR

AU - Garrido, M.ª Isabel

AU - Gómez Gil, Javier

AU - Jaramillo, Jesús Angel

TI - Homomorphisms on some function algebras.

JO - Extracta Mathematicae

PY - 1992

VL - 7

IS - 1

SP - 46

EP - 52

AB - Suppose that A is an algebra of continuous real functions defined on a topological space X. We shall be concerned here with the problem as to whether every nonzero algebra homomorphism φ: A → R is given by evaluation at some point of X, in the sense that there exists some a in X such that φ(f) = f(a) for every f in A. The problem goes back to the work of Michael [19], motivated by the question of automatic continuity of homomorphisms in a symmetric *-algebra. More recently, the problem has been considered by several authors, mainly in the case of algebras of smooth functions: algebras of differentiable functions on a Banach space in [2], [11], [13] and [14]; algebras of differentiable functions on a locally convex space in [3], [4], [5] and [6], and algebras of smooth functions in the abstract context of smooth spaces in [18]. We shall be interested both in the general case and in the case of functions on a Banach space. This report is based on the results obtained in [8].

LA - eng

KW - Algebra de funciones; Homomorfismos; Anillos de funciones; Funcionales multiplicativos

UR - http://eudml.org/doc/39964

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.