圆环的Bergman空间上乘法算子的Thomson型定理

Thomson-type theorem for the multiplication operators on the Bergman space of the annulus

Thomson定理指出,如果h在闭单位圆盘上解析,则存在有限Blaschke积B使得h可以写成B的函数,且在单位圆盘的Bergman空间上h诱导的乘法算子Th的换位等于乘法算子TB的换位.本文在适当条件下将Thomson定理推广到圆环上的Bergman空间.此外,本文也考虑了相应乘法算子的约化子空间.

Thomson's theorem implies that on the Bergman space over the unit disk if h is holomorphic on the closed unit disk,then there is a nite Blaschke product B such that h can be written as a function of B,and the commutant of the multiplication operator Mh by h equals that of MB.This is essentially generalized to the Bergman space over an annulus under a mild condition.It is also seen that the situation is complicated compared with the classical Bergman space over the unit disk.We also consider the associated reducing subspaces of the concerned multiplication operators.