Multiplicative ∗-lie triple higher derivations of standard operator algebras

Abstract

Let be a standard operator algebra on an infinite dimensional complex Hilbert space containing identity operator I. In this paper it is shown that if is closed under the adjoint operation, then every multiplicative ∗-Lie triple derivation is a linear ∗-derivation. Moreover, if there exists an operator S ∈ such that S + S∗ = 0 then d(U) = U S − SU for all U ∈ , that is, d is inner. Furthermore, it is also shown that any multiplicative ∗-Lie triple higher derivation D = {δn}n∈ℕ of is automatically a linear inner higher derivation on with d(U)∗ = d(U∗).