Homomorphisms on some function algebras.

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

Extracta Mathematicae, Tome 7 (1992), p. 46-52 / Harvested from Biblioteca Digital de Matemáticas

Résumé

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].

Détail

Publié le : 1992-01-01

MR MR1203441

DMLE-ID : 2631