m--isometric composition operators on directed graphs with one circuit

Abstract

The aim of this paper is to investigate $m$--isometric composition operators on directed graphs with one circuit. We establish a characterization of $m$--isometries and prove that complete hyperexpansiveness coincides with $2$--isometricity within this class. We discuss the $m$--isometric completion problem for unilateral weighted shifts and for composition operators on directed graphs with one circuit. The paper is concluded with an affirmative solution of the Cauchy dual subnormality problem in the subclass with circuit containing one element.

arXiv comment23 pages

References in corpus (2)

• Analytic $m$-isometries without the wandering subspace property
• m-isometric operators and their local properties