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Homomorphisms between algebras of continuous functions.

Llavona, José G. and Jaramillo Aguado, Jesús Ángel (1989) Homomorphisms between algebras of continuous functions. Canadian Journal of Mathematics-Journal Canadien de Mathématiques, 41 (1). pp. 132-162. ISSN 0008-414X

Official URL: http://cms.math.ca/10.4153/CJM-1989-007-8

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Abstract

We begin this paper with a general study of algebra homomorphisms between algebras of continuous real functions on completely regular topological spaces; we study their
automatic continuity and we characterize them as induced by continuous maps; then we give conditions on the inducing maps for the corresponding composition subalgebras
to be dense or closed. These general results apply to the case of algebras of weakly continuous and weakly uniformly continuous functions on bounded subsets of a Banach
space. We also study, as an application, the problem of interpolating bounded sequences of a Banach space by weakly uniformly continuous functions.


Item Type:Article
Uncontrolled Keywords:Algebra homomorphisms between algebras of continuous real functions on completely regular topological spaces; Automatic continuity; Composition subalgebras; Algebras of weakly continuous and weakly uniformly continuous functions on bounded subsets of a Banach space; Interpolating bounded sequences of a Banach space by weakly uniformly continuous functions
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16416
Deposited On:18 Sep 2012 08:34
Last Modified:06 Nov 2013 17:24

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