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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,...
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