论文标题
几乎不变的子空间，应用程序截断了toeplitz操作员
Nearly invariant subspaces with applications to truncated Toeplitz operators
论文作者
论文摘要
在本文中，我们首先研究了具有有限缺陷的标量和矢量值接近不变子空间的结构。然后，我们随后为我们的新结果提供了一些富有成果的应用。我们为具有有限缺陷的矢量值几乎不变子空间产生分解定理。更具体地说，我们显示每个具有有限缺陷的矢量值接近不变的子空间可以写成向后移动不变子空间的等距图像。我们还表明，矢量值接近不变子空间与具有有限缺陷的标量价值接近不变子空间之间存在联系。这是一个有力的结果，它使我们能够使用矢量值耐力空间技术来了解耐力空间的标量子空间的结构。这些结果具有遥远的应用程序，特别是它们使我们能够开发出：研究核的研究：Toeplitz操作员，截断的Toeplitz操作员，截断的Toeplitz Operator在多沿空间上的Toeplitz操作员和双重截断的Toeplitz toeplitz操作员。
In this paper we first study the structure of the scalar and vector-valued nearly invariant subspaces with a finite defect. We then subsequently produce some fruitful applications of our new results. We produce a decomposition theorem for the vector-valued nearly invariant subspaces with a finite defect. More specifically, we show every vector-valued nearly invariant subspace with a finite defect can be written as the isometric image of a backwards shift invariant subspace. We also show that there is a link between the vector-valued nearly invariant subspaces and the scalar-valued nearly invariant subspaces with a finite defect. This is a powerful result which allows us to gain insight in to the structure of scalar subspaces of the Hardy space using vector-valued Hardy space techniques. These results have far reaching applications, in particular they allow us to develop an all encompassing approach to the study of the kernels of: the Toeplitz operator, the truncated Toeplitz operator, the truncated Toeplitz operator on the multiband space and the dual truncated Toeplitz operator.
