On unitary equivalence and reducing subspaces of analytic Toeplitz operator on vector-valued Hardy space

Cui Chen; Yucheng Li; Ya Wang

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arXiv · 2409.07112

On unitary equivalence and reducing subspaces of analytic Toeplitz operator on vector-valued Hardy space

Cui Chen·Yucheng Li·Ya Wang

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Abstract

In this paper, we proved that $T_{z^n}$ acting on the $\mathbb{C}^m$-valued Hardy space $H_{\mathbb{C}^m}^2(\mathbb{D})$, is unitarily equivalent to $\bigoplus_1^{mn}T_z$, where $T_z$ is acting on the scalar-valued Hardy space $H_{\mathbb{C}}^2(\mathbb{D})$. And using the matrix manipulations combined with operator theory methods, we completely describe the reducing subspaces of $T_{z^n}$ on $H_{\mathbb{C}^m}^2(\mathbb{D})$.

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BibTeX RIS

Cui Chen, Yucheng Li, Ya Wang. 2024-09-11. On unitary equivalence and reducing subspaces of analytic Toeplitz operator on vector-valued Hardy space. https://arxiv.org/abs/2409.07112

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