加权Hardy空间上算子序列的收敛性

The Convergence of Sequence of Operators on Weighted Hardy Spaces

设D为复平面C中的开单位圆盘,φ:D→D解析,ψ:D→C,Cψ,φ是H2(β)上的加权复合算子,S是加权移位算子.该文通过讨论算子序列{S*nCψ,φSn}n∞=1与{S*nC*ψ,φSn}n∞=1的收敛性来研究H2(β)上加权复合算子Cψ,φ的渐近Toep litz性.

Let φ be a holomorphic self - map of unit disk D in C, ψ be a holomorphic function on D and Cψ,φ be a weighted composition operator on H^2 （β）. In this paper, we discuss the asymptotic Toeplitzness of weighted composition operators by studying the convergence of sequence of operators {S^＊nCψ,φS^n}n=1^∞ and {S^＊nCψ,φ^＊S^n}n=1^∞.