## Isometries on the $\ell^1$-sum of $C_0(Î©,E)$ type spaces

J. Math. Sci. Univ. Tokyo
Vol. 2 (1995), No. 1, Page 131--154.

Wang, Risheng ; Orihara, Akio
Isometries on the $\ell^1$-sum of $C_0(Î©,E)$ type spaces
In this paper, we study the representations of isometries on the unit sphere of the $\ell\sp 1$-sum of $C\sb 0 (Î©,E)$ type spaces and give an affirmative answer to the corresponding Tingley's problem. Especially, we can get the results of [1].
Keywords: Isometry; $\ell\sp p$-sum; Tingley's problem; Mazur-Ulam's theorem