Nearly invariant subspaces and kernels of Toeplitz operators on the Hardy space over the bidisk

Fuente: arXiv
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Main Authors: Zhu, Senhua, Liang, Yuxia
Format: Preprint
Published: 2024
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_version_ 1866918142695964672
author Zhu, Senhua
Liang, Yuxia
author_facet Zhu, Senhua
Liang, Yuxia
contents In this paper, the analysis of nearly invariant subspaces and kernels of Toeplitz operators on the Hardy space over the bidisk is developed. Firstly, we transcribe Chalendar, Chevrot and Partington's result to vector-valued Hardy space $H^{2}_{\ma{H}}(\mathbb{D})$ when $\ma{H}$ is an infinite dimensional separable complex Hilbert space. Secondly, we explore the definition of nearly invariant subspaces on Hardy space over the bidisk, and apply it to characterize kernels of Toeplitz operators. Finally, we define the nearly invariant subspaces for commutative isometric tuples, which allows us to show that the kernel of general Toeplitz operators is also nearly invariant.
format Preprint
id arxiv_https___arxiv_org_abs_2408_05991
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Nearly invariant subspaces and kernels of Toeplitz operators on the Hardy space over the bidisk
Zhu, Senhua
Liang, Yuxia
Functional Analysis
In this paper, the analysis of nearly invariant subspaces and kernels of Toeplitz operators on the Hardy space over the bidisk is developed. Firstly, we transcribe Chalendar, Chevrot and Partington's result to vector-valued Hardy space $H^{2}_{\ma{H}}(\mathbb{D})$ when $\ma{H}$ is an infinite dimensional separable complex Hilbert space. Secondly, we explore the definition of nearly invariant subspaces on Hardy space over the bidisk, and apply it to characterize kernels of Toeplitz operators. Finally, we define the nearly invariant subspaces for commutative isometric tuples, which allows us to show that the kernel of general Toeplitz operators is also nearly invariant.
title Nearly invariant subspaces and kernels of Toeplitz operators on the Hardy space over the bidisk
topic Functional Analysis
url https://arxiv.org/abs/2408.05991