## Abstract

This paper contains a further analysis of the Toeplitz-like operators T_{ω} on H^{p} with rational symbol ω having poles on the unit circle that were previously studied in Groenewald (Oper Theory Adv Appl 271:239–268, 2018; Oper Theory Adv Appl 272:133–154, 2019). Here the adjoint operator Tω∗ is described. In the case where p= 2 and ω has poles only on the unit circle T, a description is given for when Tω∗ is symmetric and when Tω∗ admits a selfadjoint extension. If in addition ω is proper, it is shown that Tω∗ coincides with the unbounded Toeplitz operator defined by Sarason (Integr Equ Oper Theory 61:281–298, 2008) and studied further by Rosenfeld (Classes of densely defined multiplication and Toeplitz operators with applications to extensions of RKHS’s, 2013; J Math Anal Appl 440:911–921, 2016).

Original language | English |
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Article number | 43 |

Pages (from-to) | 1-23 |

Number of pages | 23 |

Journal | Integral Equations and Operator Theory |

Volume | 91 |

Issue number | 5 |

Early online date | 24 Sept 2019 |

DOIs | |

Publication status | Published - Oct 2019 |

### Funding

This work is based on research supported in part by the National Research Foundation of South Africa. Any opinion, finding and conclusion or recommendation expressed in this material is that of the authors and the NRF does not accept any liability in this regard. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Funders | Funder number |
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National Research Foundation | |

National Research Foundation |

## Keywords

- Adjoint
- Symmetric operators
- Toeplitz operators
- Unbounded operators