关键词: 加权复合算子, Fredholm 算子, Bers型空间, 闭值域, 有界性, 弱紧性

Abstract: 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.

Key words: Weighted composition operator, Fredholm operator, Bers-type space, Closed range, Boundedness, Weak compactness