Bounded point evaluation for operators with the wandering subspace property

Abstract

We extend and study the notion of bounded point evaluation introduced by Williams for a cyclic operator to the class of operators with the wandering subspace property. We characterize the set bpe(T ) of all bounded point evaluations for an operator T with the wandering subspace property in terms of the invertibility of certain projections. This result generalizes the earlier established characterization of bpe(T ) for a finitely cyclic operator T . Further, if T is a left-invertible operator with the wandering subspace property, then we determine the bpe(T ) and the set abpe(T ) of all analytic bounded point evaluations for T . We also give examples of left-invertible operator T with the wandering subspace property for which D 0, r(T ′ ) −1 abpe(T ) ⊆ bpe(T ), where r(T ′ ) is the spectral radius of the Cauchy dual T ′ of T .