Multiplicative ∗-lie triple higher derivations of standard operator algebras

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