Bergman Kernel Estimates and Toeplitz Operators on Holomorphic Line Bundles

Document Type : Original Article

Author

Said Asserda

Ibn tofail University, Faculty of Sciences, Department of Mathematics, P.O.Box 242, Kenitra, Morocco.

10.22034/kjm.2016.41044

Abstract

We characterize operator-theoretic properties
(boundedness, compactness, and Schatten class membership) of Toeplitz
operators with positive measure symbols on Bergman spaces of holomorphic hermitian line bundles over Kähler Cartan-Hadamard manifolds in terms of geometric or operator-theoretic properties of measures.

Keywords

Toeplitz operator

Bergman space

line bundle

Schatten class

Subjects

• 30 Functions of a complex variable
• 32 Several complex variables and analytic spaces
• 47 Operator theory

---