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A special version of the Schwarz lemma on an infinite dimensional domain

Tatsuhiro Honda — 1997

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $B$ be the open unit ball of a Banach space $E$ , and let $f : B \to B$ be a holomorphic map with $f (0) = 0$ . In this paper, we discuss a condition whereby $f$ is a linear isometry on $E$ .

A characterization of linear automorphisms of the Euclidean ball

Hidetaka Hamada; Tatsuhiro Honda — 1999

Annales Polonici Mathematici

Let B be the open unit ball for a norm on $ℂ^{n}$ . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on $ℂ^{n}$ . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.

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