Antinormality and m-isometry of shift on weighted trees

Abstract

The shift operator and its various generalizations are amongst the most widely studied operators on a Hilbert space. In this paper, we characterize antinormal and m-isometric shift operator S on the Hilbert space L2(T, λ) associated with a locally finite directed weighted tree T. We also discuss interesting connections between antinormality and m-isometry of S. © 2022, The Author(s).