## 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 |

## Keywords

- Adjoint
- Symmetric operators
- Toeplitz operators
- Unbounded operators