A hypercyclic finite rank perturbation of a unitary operator

Stanislav Shkarin

A hypercyclic finite rank perturbation of a unitary operator

Functional Analysis 2010-08-23 v1

Authors: Stanislav Shkarin

Abstract

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space $\H$ are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.

Keywords

hypercyclic operator finite rank perturbation unitary operator hyponormal operator supercyclicity

Cite

@article{arxiv.1008.3490,
  title  = {A hypercyclic finite rank perturbation of a unitary operator},
  author = {Stanislav Shkarin},
  journal= {arXiv preprint arXiv:1008.3490},
  year   = {2010}
}

Comments

published in Mathematische Annalen

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