The Relationship between Model Spaces and Invariant Subspaces of the Unilateral Shift Operator
Xiaoyuan Yang · Contemporary Mathematics · 2024
Let u be an inner function and K 2 u be the model space.For inner function v, the space vH 2 is the invariant subspace of the unilateral shift operator on H 2 .In this article, the relationship between model spaces K 2 u and invariant subspaces vH 2 of the unilateral shift operator is discussed from perspectives of the Toeplitz kernels kerT uv (v = u), the spectrum of u and v, the left invertible property of T uv , the minimal isometric dilation and the completeness problem.We obtain that the Toeplitz operator T u on H 2 is a minimal isometric dilation of A v u defined on the model space