Elementary maps on nest algebras

Let A1, A2 be algebras and let M : A1 →A2, M∗ : A2 →A1 be maps. An elementary map of A1 ×A2 is an ordered pair (M,M∗) such that M(AM∗(B)C) =M(A)BM(C), M∗(BM(A)D) =M∗(B)AM∗(D) for all A,C ∈ A1, B,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. © 2005 Elsevier Inc. All rights reserved