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
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)
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.
