Characterizations of isomorphisms and derivations of some algebras

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