Berezin Transform And Algebraic Properties Of Toeplitz Operators On The Bergman Space

In this paper,we mainly study the Berezin Transform on the Bergman space and further extend Ahern’s theorem and apply the extended Ahern’s theorem to study algebraic properties of Toeplitz operators.In the first chapter, we discuss some relevant research background and give main results.In the second chapter, we introduce some preliminary knowledge.In the third chapter, we obtain the extended Ahern’s Theorem.In the fourth chapter, we apply the extended Ahern’s theorem to study alge-braic properties of Toeplitz operator.