Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties

Abstract

Let T T be a surjective mapping from a uniform algebra A A on a compact Hausdorff space X X onto a uniform algebra on a compact Hausdorff space Y Y . Suppose that f g ( X ) = T ( f ) T ( g ) ( Y ) fg(X)=T(f)T(g)(Y) holds for every f , g ∈ A f,g\in A . Then we have that T T is an almost isometric isomorphism, which is a generalization of results of Molnár (2002) and Rao and Roy (2005).