Homomorphisms of weighted algebras of continuous functions

Summary

A characterization is given of all continuous algebra homomorphisms H from the weighted space of continuous functions CV(X, E) into ℂ, where X is a completely regular Hausdorff space, E a locally convex algebra and V a family of weight functions that vanish at infinity. These homomorphisms are represented in the form H(f) = h(f(x)) with x in X and h a continuous algebra homomorphism on E. We then consider the space of homomorphisms of CV(X, E) and give some counterexamples to possible further generalizations.

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Entrata in Redazione il 18 febbraio 1977.

« Aspirant » of the Belgian « Nationaal Fonds voor Wetenschappelijk Onderzoek ».

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Govaerts, W. Homomorphisms of weighted algebras of continuous functions. Annali di Matematica 116, 151–158 (1978). https://doi.org/10.1007/BF02413872

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Keywords

  • Continuous Function
  • Weight Function
  • Weighted Space
  • Hausdorff Space
  • Algebra Homomorphism