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

Volume 37 / 1996

Binyamin Schwarz, Uri Srebro 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.

Authors

  • Binyamin Schwarz
  • Uri Srebro

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