Abstract
Let be a standard operator algebra on an infinite dimensional complex Hilbert space
containing identity operator I. Let
be the polynomial defined by n indeterminates
and their multiple *-Lie products and
be the set of non-negative integers. In this paper, it is shown that if
is closed under the adjoint operation and
is the family of mappings
such that
the identity map on
satisfying
for all
and for each
, then
is an additive *-higher derivation. Moreover,
is inner.