For a shift operator T with finite multiplicity acting on a separable infinite dimensional Hilbert space we represent its nearly \(T^{-1}\) invariant subspaces in Hilbert space in terms of invariant subspaces under the backward shift. Going further, given any finite Blaschke product B, we give a description of the nearly \(T_{B}^{-1}\) invariant subspaces for the operator \(T_B\) of multiplication by B in a scale of Dirichlet-type spaces.

中文翻译：

---

希尔伯特空间中算子的几乎不变子空间

对于作用在可分离的无限维希尔伯特空间上的具有有限多重性的移位算子T，我们用向后移位下的不变子空间表示希尔伯特空间中其接近\（T ^ {-1} \）不变子空间。更进一步，给定任何有限的Blaschke乘积B，我们以Dirichlet-的规模描述乘以B的算子\（T_B \）的几乎\（T_ {B} ^ {-1} \）不变子空间。输入空格。