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 M z be the minimal normal extension on a separable complex Hilbert space K containing H . Let b p e ( S ) be the set of bounded point evaluations and let a b p e ( S ) be the set of analytic bounded point evaluations. We show a b p e ( S ) = b p e ( S ) ∩ I n t ( σ ( S ) ) . The result affirmatively answers a question asked by J. B. Conway concerning the equality of the interior of b p e ( S ) and a b p e ( S ) for a rationally multicyclic subnormal operator S . As a result, if λ 0 ∈ I n t ( σ ( S ) ) and d i m ( k e r ( S − λ 0 ) ⁎ ) = N , where N is the minimal number of cyclic vectors for S , then the range of S − λ 0 is closed, hence, λ 0 ∈ σ ( S ) ∖ σ e ( S ) . [ABSTRACT FROM AUTHOR]