Hypercyclic Toeplitz Operators

Abstract

We study hypercyclicity of the Toeplitz operators in the Hardy space \({H^{2}(\mathbb{D})}\) with symbols of the form \({p(\overline{z}) + \varphi(z)}\), where \({p}\) is a polynomial and \({\varphi \in H^{\infty}(\mathbb{D})}\). We find both necessary and sufficient conditions for hypercyclicity which almost coincide in the case when deg \({p =1}\).

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Correspondence to Anton Baranov.

Additional information

The authors were supported by the Grant MD-5758.2015.1. A. Lishanskii was partially supported by JSC “Gazprom Neft” and by RFBR Grant 14-01-31163.

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Baranov, A., Lishanskii, A. Hypercyclic Toeplitz Operators. Results. Math. 70, 337–347 (2016). https://doi.org/10.1007/s00025-016-0527-x

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Mathematics Subject Classification

  • 47A16
  • 47B35
  • 30H10

Keywords

  • Hypercyclic operator
  • Toeplitz operator
  • univalent function