Carathéodory balls and norm ball of the domains \(H_ n = \{ z\in\mathbb{C}^ n: | z_ 1| +\cdots +| z_ n| <1\}\)
Let \(N_ n(z) = | z_ 1 | + \dots + | z_ n |\) and let \[ H_ n = \{z \in C^ n : \;N_ n(z) < 1\}. \] It is proved that the only Carathéodory balls in \(H_ n\), which are norm balls, are those centered at the origin. It is noted that the same result is proved in a paper by U. Srebro in the same volume.
scientific article; zbMATH DE number 755538