论文标题
研究希尔伯特空间中有有限缺陷的几乎不变子空间
Study of nearly invariant subspaces with finite defect in Hilbert spaces
论文作者
论文摘要
在本文中，我们简要地描述了几乎$ t^{ - 1} $不变子空间，有限缺陷，用于换档操作员$ t $具有有限多重性，该元素在可分离的Hilbert Space $ \ Mathcal $ \ Mathcal {h h} $中，作为几乎$ t^{-1} $ novariant子空间的概括，由liang和parting contonton conding conting conting yp condists conting。换句话说，我们表征了几乎$ t^{ - 1} $不变子空间，该子空间具有有限的缺陷，该子空间在向量值为hardy空间中的向后移动不变子空间中使用\ cite {cdp}中的定理3.5。此外，我们还提供了几乎$ t_b^{ - 1} $不变子空间的具体表示，具有有限缺陷，以dirichlet-type spaces $ \ mathcal {d}_α$ for $α\ in [-1,1] $ in [-1,1] $对应于任何有限的Blashcke blashcke Product $ b $ b $ b $ b $ b $。
In this article, we briefly describe nearly $T^{-1}$ invariant subspaces with finite defect for a shift operator $T$ having finite multiplicity acting on a separable Hilbert space $\mathcal{H}$ as a generalization of nearly $T^{-1}$ invariant subspaces introduced by Liang and Partington in \cite{YP}. In other words we characterize nearly $T^{-1}$ invariant subspaces with finite defect in terms of backward shift invariant subspaces in vector-valued Hardy spaces by using Theorem 3.5 in \cite{CDP}. Furthermore, we also provide a concrete representation of the nearly $T_B^{-1}$ invariant subspaces with finite defect in a scale of Dirichlet-type spaces $\mathcal{D}_α$ for $α\in [-1,1]$ corresponding to any finite Blashcke product $B$.
