We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules over a unital C^＊-algebra. The main purpose of this paper is to investigate N-isometric C^＊-algebra isomorphisms between l...We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules 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 t：heir N-isometric homomorphisms.展开更多
基金The first author is supported by Korea Research Foundation Grant KRF-2005-041-C00027
文摘We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules 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 t：heir N-isometric homomorphisms.
