Characterizations of isomorphisms and derivations of some algebras

Let phi be a zero-product preserving bijective bounded linear map from a unital algebra A onto a unital algebra B such that phi(1) = k. We show that if A is a CSL algebra on a Hilbert space or a J-lattice algebra on a Banach space then there exists an isomorphism psi from A onto B such that phi = k psi. For a nest algebra A in a factor von Neumann algebra, we characterize the linear maps on A such that delta(x)y + x delta (y) = 0 for all x, y is an element of A with xy = 0. (C) 2006 Elsevier Inc. All rights reserved.