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arXiv · 2411.13177

Almost invariant subspaces of shift operators and products of Toeplitz and Hankel operators

Caixing Gu·In Sung Hwang·Hyoung Joon Kim·Woo Young Lee·Jaehui Park
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Abstract

In this paper we formulate the almost invariant subspaces theorems of backward shift operators in terms of the ranges or kernels of product of Toeplitz and Hankel operators. This approach simplifies and gives more explicit forms of these almost invariant subspaces which are derived from related nearly backward shift invariant subspaces with finite defect. Furthermore, this approach also leads to the surprising result that the almost invariant subspaces of backward shift operators are the same as the almost invariant subspaces of forward shift operators which were treated only briefly in literature.

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Caixing Gu, In Sung Hwang, Hyoung Joon Kim, Woo Young Lee, Jaehui Park. 2024-11-20. Almost invariant subspaces of shift operators and products of Toeplitz and Hankel operators. https://arxiv.org/abs/2411.13177

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