Geodesic
On isometrical extension properties of function spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 1, pp. 105-115.

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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.
DOI : 10.14712/1213-7243.015.109
Classification : 46B04, 54C35, 54H20
Keywords: linear extension of isometry; theorem of Banach and Mazur; Hilbert cube; Cantor set 
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Kato, Hisao. On isometrical extension properties of function spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 1, pp. 105-115. doi : 10.14712/1213-7243.015.109. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.015.109/

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