Abstract. We show that operators on Hilbert space in the dual operator algebra class ${\msbm A}_{n}$ have as the compression to a semi-invariant subspace, and up to unitary equivalence, both any diagonal operator on $n$ dimensional space with eigenvalues in the open unit disk and a certain block upper triangular operator. From the latter compression follows the construction of some sequences of vectors yielding point evaluations for analytic functions of the original operator.

AMS Subject Classification (1991): 47D27, 47A20

Received November 10, 1993 and in revised form November 1, 1994. (Registered under 5604/2009.)