单位球上加权Banach空间中的Toeplitz算子(英文)

The Toeplitz Operators on the Weighted Banach Space of the Unit Ball

应用Berezin变换的方法对单位球上加权Banach空间中的Toeplitz算子进行刻画,对正函数的情形,将现有的单位圆的相关结论推广至单位球,得到Toeplitz算子连续的充分必要条件,并给出Toeplitz算子为紧算子的充分条件.

In the case of positive symbols,the continuity and compactness of a Toeplitz operator are character-ized. The Toeplitz operator under investigation acts upon the weighted Banach space H∞U which consists of analytic functions on the unit ball of Cn . Our characterizations are in terms of the Berezin transform.