Abstract. Let $\{D_n\} $ be a sequence of bounded invertible operators on a Hilbert space ${\cal H}$. It is shown that the collection of operators $T$ for which the norm-limit $\lim D_nTD_n^{-1}$ exists is an algebra. Furthermore, some sufficient conditions on this sequence are established for the corresponding algebra to have a nontrivial invariant subspace. By considering specific sequences of operators several invariant subspace results are obtained.

AMS Subject Classification (1991): 47A15

Received December 3, 1998, and in revised form September 13, 1999. (Registered under 2735/2009.)