ON FUNCTIONAL EQUATION RELATED TO (m, n)-JORDAN TRIPLE CENTRALIZERS

In this paper, we prove the following result. Let X be a Banach space over the real or complex field F, let L(X) be the algebra of all bounded linear operators on X, and let A(X) subset of L(X) be a standard operator algebra. Suppose there exists an additive mapping T : A(X) -> L(X) satisfying the relation 2(m + n)T-2(A(p)) = (2m(2)+2mn)T(A)A(p-1)-mnT(A(p-2))A(2)+ 2mnAT(A(p-2))A - mnA(2)T(A(p-2)) + (2n(2) + 2mn)A(p-1)T(A) for all A is an element of A(X), where m >= 1, n >= 1, p >= 2 are some fixed integers. In this case T is of the form T(A) = lambda A for all A is an element of A(X) and some fixed lambda is an element of F. In particular, T is continuous.