中文摘要：

将在算子范数拓扑的意义下,研究多复变量函数的Hilbert空间之间的有界加权复合算子族的拓扑连通性.利用类似的方法还将研究在Hilbert-Schmidt范数拓扑下的连通性.这些讨论与结论适用于多种多复变量函数空间,比如Hardy空间,Bergman空间Dirichlet空间之间的加权复合算子族的拓扑结构的研究.

英文摘要：

The topological connectedness of weighted composition operators between the Hilbert spaces in several com- plex variables are studied. These results are applied to characterize the topological structure of weighed composition op- erators acting between Hardy spaces, Bergman spaces and Dirichlet spaces of several complex variables holomorphic fhnc- tions, which generalizes the results of T. Hosokawa, K. Izuchi and S. Ohno.