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Title: Perturbations of $C^{1}$ norms and associated isometry groups (Researches on isometries from various viewpoints)
Authors: Kawamura, Kazuhiro
Author's alias: 川村, 一宏
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: 108
End page: 114
Abstract: This note announces a recent result on isometries of C^{1}-function spaces over compact Riemannian manifolds [7]. We characterize isometries (with respect to certain norms inducing the C^{1}-topology) of the C^{1}-function spaces over compact Riemannian manifolds as generalized weighted composition operators, under some regularity assumption. We also apply the characterization to study continuous deformations of isometry groups induced by perturbations of norms on the function spaces.
Appears in Collections:2035 Researches on isometries from various viewpoints

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