Bounded point evaluations for rationally multicyclic subnormal operators

Let S be a pure bounded rationally multicyclic subnormal operator on a separable complex Hilbert space H and let Mz be the minimal normal extension on a separable complex Hilbert space K containing H. Let bpe(S) be the set of bounded point evaluations and let abpe(S) be the set of analytic bounded point evaluations. We show abpe(S)=bpe(S)∩Int(σ(S)). The result affirmatively answers a question asked by J. B. Conway concerning the equality of the interior of bpe(S) and abpe(S) for a rationally multicyclic subnormal operator S. As a result, if λ0∈Int(σ(S)) and dim(ker(S−λ0)⁎)=N, where N is the minimal number of cyclic vectors for S, then the range of S−λ0 is closed, hence, λ0∈σ(S)∖σe(S).