Introduction to Operator Theory on Function Spaces

Author: Qian Renyi
Publisher:
Publish Date: 2007-01-01
Features: This book primarily discusses operator theory on function spaces, providing a foundational platform for young scholars to enter this research field. It introduces key results in operator theory involving operator matrices, such as the Douglas criterion and the Cholesky factorization theorem. The book also presents a detailed exploration of the de Branges—Rovnyank method for operator theory on the H2 space. Additionally, it covers the fundamental theory of Bergman spaces and their associated operator theory, with a particular focus on the compactness of Toeplitz-type operators. It introduces the powerful tool of Berezin transforms for studying the compactness of operators on reproducing kernel spaces. The book also includes recent research findings. The intended readership includes senior undergraduate and graduate students, teachers, and scientific and technical workers in related fields of mathematics.