Bergman空间上一类斜Toeplitz算子的不变子空间

Invariant Subspaces of a Class of Slant Toeplitz Operators on the Bergman Space

本文研究了单位圆盘的Bergman空间上斜Toeplitz算子的不变子空间问题,分别利用m和p1,p2,⋯,pn的奇偶性和大小关系充分描述了Bergman空间的有限维子空间span{zp1,zp2,⋯,zpn}是以函数φ(z)=zm为符号的斜Toeplitz算子Bφ及其共轭算子Bφ∗的不变子空间的充要条件,以及该子空间何时是算子Bφ的约化子空间,这将有利于对算子Bφ结构特征的认识。

In this paper we study the problem of invariant subspaces of slant Toeplitz operators on the Bergman space of the unit disk, and respectively describe the necessary and sufficient condition for the finite dimensional subspacesspan{zp1,zp2,⋯,zpn}of Bergman space to be invariant subspaces of slant Toeplitz operatorsBφand their conjugate operatorsBφ∗with symbolφ(z)=zmby utilizing the parity and size relationship of m andp1,p2,⋯,pn, as well as when this subspace is a reducing subspace of the operatorBφ. This will benefit the knowledge of the structural features of the operatorBφ.