The paper proves realization, interpolation, extension, and Toeplitz corona theorems for the hexablock, recovering the tetrablock and biball results as special cases.
A Toeplitz corona theorem for the pentablock and applications
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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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Function theory of the hexablock and applications to the tetrablock and Euclidean biball
The paper proves realization, interpolation, extension, and Toeplitz corona theorems for the hexablock, recovering the tetrablock and biball results as special cases.