Bounded point evaluation for operators with the wandering subspace property
Trivedi Trivedi · Journal of Operator Theory · 2023
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. Further, we determine bpe(T) and abpe(T) for a left-invertible operator T with the wandering subspace property. We also give examples of left-invertible operators 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.