报告题目: Fundamental and spectral properties of Toeplitz operators on Bergman and Fock spaces
报告人: Dr. Jani Virtanen (University of Reading)
I discuss some recent results on boundedness and compactness of (generalized) Toeplitz operators acting on Bergman spaces of the unit disk and on Fock spaces of the complex plane, and state some related open problems; in particular, there is still no complete characterization of bounded Toeplitz operators on Bergman spaces.
While spectral theory of Toeplitz operators on Hardy spaces is well understood, much less is known about them in Bergman and Fock spaces. In particular, there are very few results on Fredholmness of Toeplitz operators on Fock spaces. I discuss some recent generalizations of the results in the Hilbert-Fock space to the other (generalized) Fock spaces, and list related open problems.