MULTIPLICATIVE *-LIE TRIPLE HIGHER DERIVATIONS OF STANDARD OPERATOR ALGEBRAS

摘要

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 is an element of such that S + S* = 0 then d(U) = U S - SU for all U is an element of , that is, d is inner. Furthermore, it is also shown that any multiplicative *-Lie triple higher derivation D = {delta(n)}(n is an element of N) of is automatically a linear inner higher derivation on with d(U)* = d(U*).