On isometrical extension properties of function spaces

Commentationes mathematicae Universitatis Carolinae

Hisao Kato¹ 

关键词: linear extension of isometry;    theorem of Banach and Mazur;    Hilbert cube;    Cantor set;   

DOI  :  10.14712/1213-7243.015.109

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

In this note, we prove that any ``bounded'' isometries of separable metric spaces can be represented as restrictions of linear isometries of function spaces $C(Q)$ and $C(\Delta)$, where $Q$ and $\Delta$ denote the Hilbert cube $[0,1]^{\infty}$ and a~Cantor set, respectively.

【 授权许可】

CC BY