A hypercyclic rank one perturbation of a unitary operator

TL;DR

This paper demonstrates the existence of a specific type of perturbation to a unitary operator that makes it hypercyclic, expanding understanding of operator dynamics in infinite-dimensional spaces.

Contribution

It introduces a rank one perturbation of a unitary operator that is proven to be hypercyclic, a novel example in operator theory.

Findings

Existence of a hypercyclic rank one perturbation of a unitary operator

Construction method for such perturbations

Implications for operator dynamics in Hilbert spaces

Abstract

We prove that there exists a rank one perturbation of a unitary operator on a complex separable infinite dimensional Hilbert space which is hypercyclic.