Jordan maps on triangular algebras

AbstractLet T be a triangular algebra and R′ be an arbitrary ring. Suppose that M:T→R′ and M∗:R′→T are surjective maps such thatM(aM∗(x)+M∗(x)a)=M(a)x+xM(a),M∗(M(a)x+xM(a))=aM∗(x)+M∗(x)afor all a∈T,x∈R′. In this paper, we give sufficient conditions on T such that both M and M∗ are additive. In particular, if T is a standard subalgebra of a nest algebra, then both M and M∗ are additive