On Lipschitz continuity with respect to the Poincaré metric of linear contractions between Möbius gyrovector spaces

Abstract

Abstract For every linear operator between inner product spaces whose operator norm is less than or equal to one, we show that the restriction to the Möbius gyrovector space is Lipschitz continuous with respect to the Poincaré metric. Moreover, the Lipschitz constant is precisely the operator norm.

Keywords

• Linear operator
• Contraction
• Lipschitz continuous
• Gyrovector space