一类解析Toeplitz算子的约化子空间与群的特征

Reducing Subspaces of a Class of Toeplitz Operators and Characters of the Group

设A_r为复平面中的圆环{z:r<|z|<1},L_a^2(A_r)为A_r上的Bergman空间.从局部逆的代数结构的新视角研究解析Toeplitz算子的约化子空间.首先证明L_a^2(A_r)上Toeplitz算子T_(z^N)的交换子的表示,再次证明zN的全体局部逆组成的集合在复合映射下是循环群,最后证明了循环群的特征与Toeplitz算子T_(z^N)的极小约化子空间是一一对应的.

Let Arbe the annuls{z：r〈｜z｜〈1}in the complex plane,La^2（Ar）be the Bergman space on Ar.In this article,the reducing subspaces of analytic Toeplitz operators T（z^N） have been studied from the algebraic structure of local inverses point of view.The commutants of T（z^N） are characterized firstly;and then it shows that the set of local inverses of zNis the cyclic groups of order N under composition;finally it is proved that the minimal reducing subspaces and characters of the cyclic group of the local inverses of zNare one-to-one correspondence.