函数空间上的一类算子方程的解

Solutions of Some Operator Equations in Function Spaces

研究由Lebesgue空间的乘法算子和Hardy空间上的Toeplitz算子所构成的Sylvester算子方程的解.利用算子的谱以及对算子性质的刻画,给出方程存在唯一解的充分条件,在此基础上得到唯一解的具体形式以及与之相关的充要条件.

In this paper,we consider solutions of Sylvester equations,which are composed of multiplication operators in Lebesgue space or Toeplitz operators in Hardy space.By using spectrum and properties of operators,sufficient conditions for the existence and uniqueness of the solution to equations are given.The formulas of the unique solution with a sufficient and necessary condition are also obtained.