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Homomorphisms on Function Algebras

Published online by Cambridge University Press:  20 November 2018

M. I. Garrido ,
J. Gómez Gil  and
J. A. Jaramillo
M. I. Garrido
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avda. Elvas, s/n 06071-Badajoz, Spain
J. Gómez Gil
Affiliation:
Departamento de Análisis Matemático, Universidad Complutense, 28040-Madrid, Spain
J. A. Jaramillo
Affiliation:
Depártamento de Andlisis Matemático, Universidad Complutense, 28040-Madrid, Spain
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Abstract

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Let A be an algebra of continuous real functions on a topological space X. We study when every nonzero algebra homomorphism φ: A → R is given by evaluation at some point of X. In the case that A is the algebra of rational functions (or real-analytic functions, or Cm-functions) on a Banach space, we provide a positive answer for a wide class of spaces, including separable spaces and super-reflexive spaces (with nonmeasurable cardinal).

Keywords

46E2554C40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 4 , 01 August 1994 , pp. 734 - 745
Copyright
Copyright © Canadian Mathematical Society 1994

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