Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^{n} :∥z∥ _{p} < 1}$
Volume 37 / 1996
Banach Center Publications 37 (1996), 75-83
DOI: 10.4064/-37-1-75-83
Abstract
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 $H_{p,n} = {z ∈ ℂ^{n}: ∥ z∥_{p} < 1 }$ which are balls with respect to the complex $l_{p}$ norm in $ℂ^{n}$ are those centered at the origin.
