Elementary maps on nest algebras

Let A1A1, A2A2 be algebras and let M:A1→A2M:A1→A2, M∗:A2→A1M∗:A2→A1 be maps. An elementary map of A1×A2A1×A2 is an ordered pair (M,M∗)(M,M∗) such that{M(AM∗(B)C)=M(A)BM(C),M∗(BM(A)D)=M∗(B)AM∗(D) for all A,C∈A1A,C∈A1, B,D∈A2B,D∈A2. In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.