The Finite Sum Problem Of The Product Of Toeplitz Operators On Bergman Space

The finite sum problem of the product of Toeplitz operators on Bergman Spaces has important algebraic significance in the study of operator theory,it exists in various directions of many disciplines,and Toeplitz operators also play an important role in practical application,and occupy an important position in the theoretical research of some mathematical fields.Because of the complexity and variability of Toeplitz operators,it is found that the finite sum problem of the product of Toeplitz operators with certain kinds of symbols need to be explored,so many domestic scholars have great interest in the research of finite the problem.This paper,inspired by relevant literature,generalizes and calculates the product limitation and problem of some Toeplitz operators in Bergman spaces,and then analyzes and proves that it is a necessary condition of zero operator.Since the normal operators have been completely characterized,there is still a lot of discussion on the hyponormality of the generalized Toeplitz operators and block Toeplitz operators.In recent years,many mathematicians have extended and explored the hynormality of the generalized Toeplitz operators and block Toeplitz operators.The main contents of this paper are as follows:Chapter one expounds the origin of the Toeplitz operator,then discusses its finite sum problem of the product of Toeplitz operators on the function space,as well as the research background and development status of the hyponormal operator.The second chapter gives a brief introduction to some preparatory knowledge in this thesis.The third chapter extenpreliminary data.The fourth chapter,on the basis of previous descriptions,a necessary condition for the subnormalization of the product of two identical Toeplitz operators in weighted Bergman space is given.In the fifth chapter,summary and prospect of this article.