2021/09/22 by Shailesh Trivedi, Trivedi, Shailesh
Mathematics · #05C20 #47B37 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 47B02 #Secondary 47A65
paper · pdf · doi:10.48550/arxiv.2109.10846
openalex publication_date 2021/09/22 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We extend and study the notion of bounded point evaluation introduced by\nWilliams for a cyclic operator to the class of operators with the wandering\nsubspace property. We characterize the set bpe(T) of all bounded point\nevaluations for an operator T with the wandering subspace property in terms\nof the invertibility of certain projections. This result generalizes the\nearlier established characterization of bpe(T) for a finitely cyclic operator\nT. Further, if T is a left-invertible operator with the wandering subspace\nproperty, then we determine the bpe(T) and the set abpe(T) of all analytic\nbounded point evaluations for T. We also give examples of left-invertible\noperator T with the wandering subspace property for which mathbb D\(0,\nr(T')-1\) subsetneqq abpe(T) \⊆ bpe(T), where r(T') is the\nspectral radius of the Cauchy dual T' of T.\n