Isometries on the $C_0 (Ω,E)$ type spaces

J. Math. Sci. Univ. Tokyo
Vol. 2 (1995), No. 1, Page 117--130.

Wang, Risheng
Isometries on the $C_0 (Ω,E)$ type spaces
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It is proved that if the unit spheres of $C\sb 0 (X,E)$ and $ C\sb 0 (Y,F)$ are isometric, then $X$ and $ Y$ are homeomorphic, and the unit spheres of $E$ and $F$ are isometric, generalizing the Banach-Stone's theorem; any isometry between the unit spheres of $C\sb 0 (X,H\sb 1 )$ and $C\sb 0 (Y,H\sb 2 )$ is necessarily the restriction of some linear isometry between $C\sb 0 (X,H\sb 1 )$ and $C\sb 0 (Y,H\sb 2 )$ (Where $X$ and $Y$ are locally compact Hausdorff spaces, $E$ and $F$ are strictly convex normed spaces and $H\sb 1$ , $ H\sb 2$ are real inner spaces).

Keywords: Isometry; Banach-Stone's theorem; Tingley's proble

Mathematics Subject Classification (1991): Primary 46A22; Secondary 46B20, 46C05, 46E15, 46E40
Mathematical Reviews Number: MR1348024

Received: 1994-04-27