Abstract
The purpose of this research is to find an extension of the renowned Chernoff theorem on standard operator algebra. Infact, we prove the following result: Let H be a real (or complex) Banach space and L(H) be the algebra of bounded linear operators on H. Let A(H) subset of L(H) be a standard operator algebra. Suppose that D : A(H) -> L(H) is a linear mapping satisfying the relation
D(A(n)B(n)) = D(A(n))B-n + A(n) D(B-n)
for all A, B is an element of A(H). Then D is a linear derivation on A(H). In particular, D is continuous. We also present the limitations on such identity by an example.