Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^{n} :∥z∥ _{p} < 1}$

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Title

Authors ¹, ¹

Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on

H_{p, n} = {z \in ℂ^{n} : ∥ z ∥_{p} < 1}

which are balls with respect to the complex

l_{p}

norm in

ℂ^{n}

are those centered at the origin.

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