Norm-linear and norm-additive operators between uniform algebras

摘要: Abstract Let A ⊂ C ( X ) and B Y be uniform algebras with Choquet boundaries δA δB. map T : → is called norm-linear if ‖ λ f + μ g = ; norm-additive, , norm-additive in modulus, | for each ∈ all algebra elements g. We show that any surjection there exists a homeomorphism ψ δ such y every . Sufficient conditions surjections, not assumed priori to linear, or continuous, unital isometric isomorphisms are given. prove which i preserves the peripheral spectra of -peaking functions A, isomorphism. In particular, we linear operator between two algebras, surjective norm-preserving, unital, functions, then it automatically multiplicative and, fact, an