Multiplicative *-Lie type higher derivations of standard operator algebras

Let A be a standard operator algebra on an infinite dimensional complex Hilbert space H containing identity operator I. Let p(n)(X-1, X-2, ... , X-n) be the polynomial defined by n indeterminates X1, ... , X-n and their multiple *-Lie products and N be the set of non-negative integers. In this paper, it is shown that if U is closed under the adjoint operation and D={d(m)}(m is an element of N) is the family of mappings d(m):U -> B(H) such that d(0)=id(U), the identity map on U satisfying d(m)(p(n)(U-1,U-2, ... ,U-n)) = Sigma(i1+i2+...+in=m) p(n)(d(i1)(U-1), d(i2)(U-2), ... , d(in)(U-n)) for all U-1,U-2, ... ,U-n is an element of U and for each m is an element of N, then D={d(m)}(m is an element of N) is an additive *-higher derivation. Moreover, D is inner.