扰动后移的不变子空间

arXiv - MATH - Operator Algebras Pub Date : 2024-07-24 DOI:arxiv-2407.17352

Soma Das, Jaydeb Sarkar

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引用次数: 0

摘要

我们表示哈代空间的封闭子空间，这些子空间在后向平移的无限阶扰动下是不变的。我们将其应用于后移几乎不变子空间的分类，并表示在后移几乎不变子空间的更精细版本下不变的封闭子空间。某些扰动托普利兹算子的核就是新引入的近不变子空间的例子。

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Invariant subspaces of perturbed backward shift

We represent closed subspaces of the Hardy space that are invariant under finite-rank perturbations of the backward shift. We apply this to classify almost invariant subspaces of the backward shift and represent closed subspaces that are invariant under a more refined version of nearly invariant subspaces of the backward shift. Kernels of certain perturbed Toeplitz operators are examples of the newly introduced nearly invariant subspaces.

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arXiv - MATH - Operator Algebras

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