Sobolev圆盘代数的不变子空间

The Invariant Subspaces of the Sobolev Disk Algebra

研究了Sobolev圆盘代数R(D)上乘自变量算子M_z的不变子空间,给出了M_z在任何不变子空间上限制的基本性质,证明了M_z分别限制在两个不变子空间上酉等价当且仅当这两个不变子空间相等,并描述了M_z的一类公共零点在边界的不变子空间的结构.

We study the invariant subspaces of the operator Mz on the Sobolev disk algebra R（D）. First, we study the multiplication operator Mz restricted to the invariant subspace. Then we show that Mz restricted to one invariant subspace is unitarily equivalent to Mz restricted to another invariant subspace if and only if the two invariant subspaces are equal. We also characterize the invariant subspaces with common zeros on the boundary of the disk.