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Title: SURJECTIVE ISOMETRIES ON $C^{1}[0,1]$ WITH RESPECT TO SEVERAL NORMS (Researches on isometries from various viewpoints)
Authors: Miura, Takeshi
Author's alias: 三浦, 毅
Keywords: 46J10
continuously differentiable function
extreme point
Issue Date: Jul-2017
Publisher: 京都大学数理解析研究所
Journal title: 数理解析研究所講究録 = RIMS Kokyuroku
Volume: 2035
Start page: 10
End page: 14
Abstract: Let C^{1}[0, 1] be a complex linear space of all continuously differentiable complex valued functions on the unit interval [0, 1]. We give a characterization of surjective, not necessarily linear, isometries on C^{1}[0, 1] with respect to the following norms: Vert fVert_{$Sigma$}=Vert fVert_{infty}+Vert f'Vert_{infty}, displaystyle Vert fVert_{C}=sup{|f(t)|+|f'(t)| : tin[0, 1]} and Vert fVert_{$sigma$}=|f(0)|+Vert f'Vert_{infty} for fin C^{1}[0, 1], respectively.
Appears in Collections:2035 Researches on isometries from various viewpoints

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