Jordan higher all-derivable points in nest algebras

摘要

Let N be a non-trivial and complete nest on a Hilbert space H. Suppose d = {d n: n ∈ N} is a group of linear mappings from AlgN into itself. We say that d = {d _n: n ∈ N} is a Jordan higher derivable mapping at a given point G if d _n(ST + TS) = Σ _(i+j=n) {d _i(S)d _j(T)+ d _j(T) d(S)} forany S,T ∈ AlgN with ST = G. An element G ∈ AlgN is called a Jordan higher all-derivable point if every Jordan higher derivable mapping at G is a higher derivation. In this paper, we mainly prove that any given point G of AlgN is a Jordan higher all-derivable point. This extends some results in [1] to the case of higher derivations.