The Berezin transform and operators on spaces of analytic functions
Volume 38 / 1997
Banach Center Publications 38 (1997), 361-380
DOI: 10.4064/-38-1-361-380
Abstract
In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz operators 6. Sarason's example
