Llavona, José G.Jaramillo Aguado, Jesús Ángel2023-06-202023-06-2019890008-414X10.4153/CJM-1989-007-8https://hdl.handle.net/20.500.14352/57533We 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.journal articlehttp://cms.math.ca/10.4153/CJM-1989-007-8http://cms.math.ca/cjm/metadata only access517.98Algebra homomorphisms between algebras of continuous real functions on completely regular topological spacesAutomatic continuityComposition subalgebrasAlgebras of weakly continuous and weakly uniformly continuous functions on bounded subsets of a Banach spaceInterpolating bounded sequences of a Banach space by weakly uniformly continuous functionsAnálisis funcional y teoría de operadores