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Homomorphisms on some function algebras

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Garrido, M. Isabel and Gómez Gil, Javier and Jaramillo Aguado, Jesús Ángel (1992) Homomorphisms on some function algebras. Extracta Mathematicae, 7 (1). pp. 46-52. ISSN 0213-8743

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Official URL: http://dmle.cindoc.csic.es/pdf/EXTRACTAMATHEMATICAE_1992_07_01_12.pdf




Abstract

For an algebra A of continuous real-valued functions on a topological space X, the question of whether every algebra homomorphism is a point evaluation for a point in X is considered. A variety of results are provided, such as the following. Let X be completely regular and A⊂C(X) a subalgebra with unit which is closed under bounded inversion and separates points and closed sets. Then every homomorphism is a point evaluation for a point in X if and only if, for each point z in the Stone-Čech compactification of X and not in X, there exists a function in A whose extension to z is infinite. Examples are considered and further results for the case of functions on a Banach space are discussed


Item Type:Article
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:21718
Deposited On:06 Jun 2013 16:38
Last Modified:12 Dec 2018 15:13

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