加权移位算子的约化子空间

Reducing Subspaces For Weighted Shift Operators

本文主要研究H_ω~2上多重加权移位算子S的约化子空间问题,通过与H_Δ~2(E)上的乘法算子M_z之间建立酉等价关系,刻画了S的约化子空间,作为应用,给出了单圆盘Bergman空间上以拟齐次函数为符号的Toeplitz算子的约化子空间和极小约化子空间的刻画。

In this paper,we mainly study the reducing subspaces for weighted shift operators S of multiplicity N on H 2ωby establishing a unitary equivalence relation between S and multiplication operator M z on H 2Δ(E).As an application,we characterize the reducing subspaces for Toeplitz operators with quasihomogeneous symbols on Bergman space over the unit disk.