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arXiv · 2606.23747

Characterization of paired and Toeplitz + Hankel operators on the polydisc

Kritika Babbar·Mo Javed·Amit Maji
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Abstract

In this paper, we obtain a complete classification of Toeplitz + Hankel operators on the vector-valued Hardy space $H^2_{\mathcal{E}}(\mathbb{D}^n)$ over the polydisc $\mathbb{D}^n$ in $\mathbb{C}^n$ for $n\geq 1$. We also characterize the paired operators on $L^2(\mathbb{T}^n)$. Furthermore, we give a complete characterization for the class of essentially Toeplitz + essentially Hankel operators on the vector-valued Hardy space $H^2_{\mathcal{E}}(\mathbb{D})$ for finite-dimensional Hilbert space $\mathcal{E}$.

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Kritika Babbar, Mo Javed, Amit Maji. 2026-06-21. Characterization of paired and Toeplitz + Hankel operators on the polydisc. https://arxiv.org/abs/2606.23747

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