Linear Maps Preserving Function Calculus and Entropies

We show that a unital map between Jordan–Banach algebras or Banach algebras that preserves function calculus given by a single nontrivial locally analytic function must be a Jordan morphism. Ramifications of this results are presented. As an application we prove that quantum channel on general Jordan \(C^{\ast}\) -algebras preserving Segal and Renyi entropy must be a Jordan homomorphism.