Disjoint hypercyclic Toeplitz operators

DEĞER Ö., ESKİŞEHİRLİ B. B.

ARCHIV DER MATHEMATIK, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s00013-024-02084-9
  • Dergi Adı: ARCHIV DER MATHEMATIK
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • İstanbul Üniversitesi Adresli: Evet

Özet

The aim of this work is to describe new classes of disjoint hypercyclic Toeplitz operators on the Hardy space H2(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H<^>2({\mathbb {D}})$$\end{document} in the unit disc D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {D}}$$\end{document}. We examine the disjoint hypercyclicity of the coanalytic Toeplitz operators, the Toeplitz operators with the symbols az+b+cz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a{\bar{z}}+b+cz$$\end{document}, where a,b,c is an element of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a,b,c\in {\mathbb {C}}$$\end{document}, and the Toeplitz operators with the symbols p(z)+phi(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(\bar{z})+\varphi (z)$$\end{document}, where p is a polynomial and phi is an element of H infinity(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi \in H<^>\infty (\mathbb {D})$$\end{document}. The hypercyclicity of these classes of Toeplitz operators has been characterized by G. Godefroy and J. Shapiro (J. Funct. Anal., 98, 1991), S. Shkarin (arXiv:1210.3191v1, 2012), and A. Baranov and L. Lishanskii (Results Math., 70, 2016), respectively. Based on their results, we first provide a criterion for the bounded linear operators to be disjoint hypercyclic. Using this criterion, we then establish certain conditions under which the aforementioned classes of Toeplitz operators are disjoint hypercyclic in terms of their symbols.