Multiplicative mappings of operator algebras

Nest algebras are the natural analogues of upper triangular matix algebras in an infinite dimensional Hilbert space. In this paper, we study multiplicative isomorphisms of subalgebras of nest algebras which contain all finite rank operators but might contain no idempotents. We prove that such multiplicative mappings are automatically additive and linear (or conjugate linear). (C) 2002 Elsevier Science Inc. All rights reserved.