Bergman空间上的复合算子的总体紧性

Collectively Compact Composition Operator Sequences on Bergman Space

刻划了具有总体紧性质的复合算子序列的符号函数,利用复合算子与Toeplitz算子的关系得到了Bergman空间上复合算子序列是总体紧算子序列的一个充分必要条件,从而推广了Smith的结果.

We give a function theoretic characterization for collectively compact composition operator sequences on Bergman space. The result shows that certain growth condition for generalized Nevanlinna counting functions of the inducing maps is necessary and sufficient for the collective compactness of composition operator sequences. The result extends W. Smith's result.