Jani Virtanen (University of Reading) : Hankel operators on the Fock space and the Berger-Coburn phenomenon

Orateur: Jani Virtanen

Affiliation : University of Reading

Date : 18 Novembre 2022

Heure : 14h

Lieu : Salle Kampé de Fériet, Bâtiment M2

Titre : Hankel operators on the Fock space and the Berger-Coburn phenomenon

Résumé : In this talk we consider Hankel operators $H_f$ on the Fock space of Gaussian square-integrable entire functions and discuss their boundedness, compactness and Schatten class properties. In particular, I focus on the following property. Given an operator ideal $M$ and a bounded function $f$, we say that the operator ideal has Berger-Coburn phenomenon (BCP) if $H_f$ is in $M$ whenever $H_{\bar f}$ is in M. One of the key differences between the Fock space, the Bergman space, and the Hardy space is that the operator ideal of compact operators on the latter two spaces has no BCP. I explain this difference and answer the question of whether the Schatten classes have BCP.