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arXiv · 2606.00850

A Toeplitz corona theorem for the pentablock and applications

Sourav Pal·Nitin Tomar
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Abstract

We state and prove a Toeplitz corona theorem for the pentablock $\mathbb{P}$, a domain in $\mathbb{C}^3$ given by \[ \mathbb{P}=\{(a_{21}, \text{tr}(A), \det(A)) \in \mathbb C^3 : A=[a_{ij}] \in M_2(\mathbb C), \|A\|<1\}. \] By two different applications of this theorem, we obtain a few new characterizations in the Toeplitz corona theorems for the bidisc and the symmetrized bidisc.

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Sourav Pal, Nitin Tomar. 2026-05-30. A Toeplitz corona theorem for the pentablock and applications. https://arxiv.org/abs/2606.00850

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