Additive mappings on operator algebras preserving absolute values

It is shown that an additive map cp : B(H) --> B(K) is the sum of two *-hom omorphisms, one of which is C-linear and the other is C-antilinear provided that (a) \phi (A)\ = phi(\A\) for all A is an element of B(H), (b) phi (I) is an orthogonal projection, and (c) phi (iI)K subset of phi (I)K. The structure of cp is more refined when it is injective, The paper also st udies the properties of cp in the absence of condition (b). Here, B(H) and B(K) denote the algebras of all (bounded linear) operators on Hilbert space s H and K, respectively. These extend a result of L, Molnar [Bull Austral, Math. Sec. 53 (1996) 391] saying an additive map cp : B(H) --> B(H) is a co nstant multiple of an either C-linear or C-antilinear *-homomorphism provid ed that (a ') \phi (A)\ = phi(\A\) for all A is an element of B(H), and (b ') phi (B(H)) contains all finite-rank operators. (C) 2001 Elsevier Science Inc, All rights reserved.