Homomorphisms on some function algebras.

Garrido, 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 -