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A Toeplitz-like operator with rational symbol having poles on the unit circle I: Fredholm properties

  • G. J. GroenewaldEmail author
  • S. ter Horst
  • J. Jaftha
  • A. C. M. Ran
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 271)

Abstract

In this paper a definition is given for an unbounded Toeplitzlike operator with rational symbol which has poles on the unit circle. It is shown that the operator is Fredholm if and only if the symbol has no zeroes on the unit circle, and a formula for the index is given as well. Finally, a matrix representation of the operator is discussed.

Keywords

Toeplitz operators unbounded operators Fredholm properties 

Mathematics Subject Classification (2010)

Primary 47B35 47A53 Secondary 47A68 

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Copyright information

© Springer Nature Switzerland AG 2018

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 MathematicsUnit for BMI, North-West UniversityPotchefstroomSouth Africa
  2. 2.Numeracy CenterUniversity of Cape TownRondeboschSouth Africa
  3. 3.Department of Mathematics, Faculty of ScienceVU Amsterdam, De Boelelaan 1081aAmsterdamThe Netherlands
  4. 4.Unit for BMI, North-West UniversityPotchefstroomSouth Africa

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