The N-isometric isomorphisms in linear N-normed C*-algebras

Abstract

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