d-isometric linear mappings in linear d-normed Banach modules

Abstract

We prove the Hyers-Ulam stability of linear d-isometries in d-normed Banach modules over a unital C*-algebra and of linear isometries in Banach modules over a unital C*-algebra. The main purpose of this paper is to investigate d-isometric C*-algebra isomorphisms between linear d-normed C*-algebras and isometric C*-algebra isomorphisms between C*-algebras, and d-isometric Poisson C*-algebra isomorphisms between linear d-normed Poisson C*-algebras and isometric Poisson C*-algebra isomorphisms between Poisson C*-algebras. We moreover prove the Hyers-Ulam stability of their d-isometric hemomorphisms and of their isometric homomorphisms.