Bloch类空间之间的加权复合算子的有界性(英文)

Boundedness of Weighted Composition Operatorsbetween Bloch-type Spaces

设H为复Hilbert空间,B(H)为H上算子范数不大于1的有界线性算子集,E=E*为B(H)中的两两可换子集.作者用E和E上的解析算子函数分别取代了复单位圆盘和复单位圆盘上的解析函数,在算子Bloch型空间上定义并讨论了加权复合算子的有界性,得到了Bα到Bβ的加权复合算子有界的充分必要条件.

Let H denote a complex Hilbert space, B （H）be bounded linear operators set on H whose norm is not more than 1, E = E^＊ be subset of B （H） whose elements are commute with each other. The author takes place of complex unit disc and analytic function in it by E and analytic operator function defined in E respectively, then defines weighted composition operators, discusses boundedness of this operator between operator Bloch-type spaces of analytic operator functions and obtains necessary and sufficient condition of boundedness of composition operator from B^α to B^β.