Publication: Homomorphisms between algebras of continuous functions.
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1989
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Canadian Mathematical Society
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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.