Characterizations of Jordan derivations on triangular rings: Additive maps Jordan derivable at idempotents
نویسندگان
چکیده
Let T be a triangular ring. An additive map δ from T into itself is said to be Jordan derivable at an element Z ∈ T if δ(A)B +Aδ(B) + δ(B)A+Bδ(A) = δ(AB+BA) for any A,B ∈ T with AB + BA = Z. An element Z ∈ T is called a Jordan all-derivable point of T if every additive map Jordan derivable at Z is a Jordan derivation. In this paper, we show that some idempotents in T are Jordan all-derivable points. As its application, we get the result that for any nest N in a factor von Neumann algebra R, every nonzero idempotent element Q satisfying PQ = Q, QP = P for some projection P ∈ N is a Jordan all-derivable point of the nest subalgebra AlgN of R.
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