不同Bers型空间之间的加权复合算子

Weighted Composition Operators between Bers-type Spaces

该文讨论了单位圆盘上不同Bers型空间之间的加权复合算子的有界性、紧性和弱紧性,给出了一些充分必要的判别条件,特别地得到不同Bers型空间上加权复合算子的紧性与弱紧性的等价性.这些推广了经典的复合算子与乘法算子的相关结论.该文同时也给出了Bers型空间上复合算子的Fredholm性和闭值域问题的刻画,完善了文献[6]中结论.

In this paper, the authors study weighted composition operators between Bers-type spaces. Some sufficient and necessary conditions for such operators to be bounded, compact and weakly compact are given, respectively. This may be regarded as a generalization of the corresponding multiplication operator and composition operator cases. As a corollary, the authors obtain that the weak compactness and the compactness of weighted composition operators between Bers-type spaces are equivalent. In addition, the authors also characterize composition operators which have Fredholm properties and closed range on Bers-type spaces, respectively.