Homomorphisms on Function Algebras

Garrido, M. I. ; Gil, J. Gómez ; Jaramillo, J. A.

Canadian journal of mathematics, Tome 46 (1994) no. 4, pp. 734-745

Résumé

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).

Détail

DOI : 10.4153/CJM-1994-041-3

Mots-clés : 46E25, 54C40

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