Isometries on the $\ell^p$-sum of $C_0(Ω, E)$ Type Spaces

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 2, Page 471--493.

Wang, Risheng
Isometries on the $\ell^p$-sum of $C_0(Ω, E)$ Type Spaces
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In this paper, we study isometries on the unit sphere of the $\ell^p$-sum of $C_0(Ω, E)$ type spaces. We obtain that any isometries on such unit sphere can be extended to be surjective real linear isometries on the whole space and give an affirmative answer to the corresponding Tingley's problem.

Keywords: Isometry, $\ell^p$-sum, Tingley's problem

Mathematics Subject Classification (1991): 46B, 46
Mathematical Reviews Number: MR1424439

Received: 1995-12-12