On unbounded Bergman operators

A note on density for the core of unbounded Bergman operators

“…The papers [4], [10], and [12] are a few to mention and contain further references on this topic. The study of unbounded Bergman operators has also been started in [4], [7], [8], and [9] . These papers deal particularly with some fundamental questions regarding the unbounded Bergman operators.…”

On self-commutators of Toeplitz operators with rational symbols

“…Observing that T ϕ belongs to the larger class of unbounded subnormal operators, one can easily prove the next lemma (see [2] for details and a proof).…”

“…In [7], the authors prove that the self-commutator of the BergmanToeplitz operator T ϕ , where the symbol ϕ is a conformal mapping of the unit disc onto a region of bounded area, has a trace class extension to L 2 a . In view of the generalization of the Berger-Shaw theorem obtained in [2], the proof given in [7] is based on the fact that D([T * ϕ , T ϕ ]) is a dense subset of L 2 a . Furthermore, using a rather technical argument, the authors were also able to establish the density of…”

The Density Problem for Self–Commutators of Unbounded Bergman Operators

“…In [5] Conway, Jin, Kouchekian prove a Berger-Shaw type theorem for an unbounded Bergman operator under the assumption that the Bergman operator and its self-commutator both have dense domains. The purpose of this paper is to investigate when the assumptions hold, i.e.…”