Generalized Hyers-Ulam-Rassias stability of n-sesquilinear-quadratic mappings on Banach modules over C*-algebras

摘要

Assume that X is a left Banach module over a unital C*-algebra A. It is shown that almost every n-sesquilinear-quadratic mapping h : X x X x X-n -> A is an n-sesquilinear-quadratic mapping when h(rx, y; z(1),..., z(n)) = h(x, ry; z(1),..., z(n)) = h(x, y; root rz(1), z(2), ..., z(n)) = (...) = h(x, y; z(1), z(2), ..., root rz(n)) = rh(x, y; z(1), z(2), ..., z(n)) (r > 0, r not equal 1) holds for all x, y, z(1),..., z(n) is an element of X.Moreover, we prove the generalized Hyers-Ulam-Rassias stability of an n-sesquilinear-quadratic mapping on a left Banach module over a unital C*-algebra. (c) 2004 Elsevier B.V. All rights reserved.