加权Bergman空间上的约化子空间

REDUCING SUBSPACES OF THE WEIGHTED BERGMAN SPACE

主要证明在加权Bergman空间上符号为有限Blaskchke乘积的解析Toeplitz算子总是可约的,即至少有一个约化子空间.并且把该算子限制在该子空间上酉等价于加权Bergman位移.

In this paper, we mainly prove that the analytic Toeplitz operator with finite Blaskchke product symbol on the weighted Bergman Spaces has at least a reducing subspace on which the restriction of the associated Toeplitz operator is unitary equivalent to the weighted Bergman shift.