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

Binyamin Schwarz; Uri Srebro — 1996

Banach Center Publications

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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Carathéodory balls and norm balls in H p , n = z ∈ ℂ n : ∥ z ∥ p < 1

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