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