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.