Toeplitz operators in Bargmann spaces
The Bargmann space is the space of the entire functions in \({\mathbb{C}}^ n,\) for which \(\int | f(z)|\) \(2e-| z|\) \(2dzd\bar z<\infty\). The author proves that the bounded Toeplitz operators in a Bargmann space are dense in the set of bounded operators with respect to the uniform topology. In the last part the author generalizes the notion of Toeplitz operator and shows that all bounded operators are generalized Toeplitz operators. The results generalize some theorems of V. Guillemin, C. A. Berger and L. Coburn.
scientific article; zbMATH DE number 4050345
scientific article