Linear preservers on upper triangular operator matrix algebras

In this paper, we obtain several characterizations of rank preserving linea r maps and completely rank nonincreasing linear maps on upper triangular Hi lbert space operator matrix algebras and apply them to get some algebraic r esults. We show that every automorphism of an upper triangular operator mat rix algebra is inner and every weakly continuous surjective local automorph ism is in fact an automorphism. A weakly continuous linear bijection on an upper triangular operator matrix algebra is idempotent preserving if and on ly if it is a Jordan homomorphism, and in turn, if and only if it is an aut omorphism or an anti-automorphism. As an application, we also obtain a resu lt concerning the asymptotic joint-similarity of matrix tuples. (C) 2001 El sevier Science Inc. All rights reserved.