A Toeplitz-like Operator with Rational Symbol Having Poles on the Unit Circle II: The Spectrum

  • G. J. GroenewaldEmail author
  • S. ter Horst
  • J. Jaftha
  • A. C. M. Ran
Part of the Operator Theory: Advances and Applications book series (OT, volume 272)


This paper is a continuation of our study of a class of Toeplitz-like operators with a rational symbol which has a pole on the unit circle. A description of the spectrum and its various parts, i.e., point, residual and continuous spectrum, is given, as well as a description of the essential spectrum. In this case, the essential spectrum need not be connected in \(\mathbb{C}\). Various examples illustrate the results.


Unbounded Toeplitz operator spectrum essential spectrum 

Mathematics Subject Classification (2010)

Primary 47B35 47A53 Secondary 47A68 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • G. J. Groenewald
    • 1
    Email author
  • S. ter Horst
    • 1
  • J. Jaftha
    • 2
  • A. C. M. Ran
    • 3
    • 4
  1. 1.Department of Mathematics Unit for BMINorth-West UniversityPotchefstroomSouth Africa
  2. 2.Numeracy CentreUniversity of Cape TownCape TownSouth Africa
  3. 3.Department of Mathematics Faculty of ScienceVU AmsterdamAmsterdamThe Netherlands
  4. 4.Unit for BMINorth-West UniversityPotchefstroomSouth Africa

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