Opuscula Math. 44, no. 3 (2024), 391-407
https://doi.org/10.7494/OpMath.2024.44.3.391

 
Opuscula Mathematica

On the Möbius invariant principal functions of Pincus

Sagar Ghosh
Gadadhar Misra

Abstract. In this semi-expository short note, we prove that the only homogeneous pure hyponormal operator \(T\) with \(\operatorname{rank} (T^*T-TT^*) =1\), modulo unitary equivalence, is the unilateral shift.

Keywords: hyponormal operator, multiplicity, trace formula, homogeneous operators, principal function.

Mathematics Subject Classification: 47B20.

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  • Sagar Ghosh
  • Indian Statistical Institute, Theoretical Statistics and Mathematics Unit, Banaglore 560 059, India
  • Gadadhar Misra (corresponding author)
  • ORCID iD https://orcid.org/0000-0001-8096-2039
  • Indian Statistical Institute, Theoretical Statistics and Mathematics Unit, Banaglore 560 059, India
  • Indian Institute of Technology Gandhinagar, Palaj, Gujarat 382 055, India
  • Communicated by Alexander Gomilko.
  • Received: 2023-04-17.
  • Revised: 2023-08-22.
  • Accepted: 2023-08-23.
  • Published online: 2024-02-15.
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Cite this article as:
Sagar Ghosh, Gadadhar Misra, On the Möbius invariant principal functions of Pincus, Opuscula Math. 44, no. 3 (2024), 391-407, https://doi.org/10.7494/OpMath.2024.44.3.391

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