On the Extension of Isometries between Unit Spheres of E and C(Ω)

In this paper, we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Naira). We obtain that if the set sm.S sub(1)(E) of all smooth points of the unit sphere S sub(1)(E) is dense in S sub(1)(E), then under some condition, every surjective isometry V s...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 19; no. 4; pp. 793 - 800
Main Author Ding, Guang Gui
Format Journal Article
LanguageEnglish
Published 01.10.2003
Subjects
Banach space
Mathematical analysis
Proving
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Summary:In this paper, we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Naira). We obtain that if the set sm.S sub(1)(E) of all smooth points of the unit sphere S sub(1)(E) is dense in S sub(1)(E), then under some condition, every surjective isometry V sub(0) from S sub(1)(E) onto S sub(1)(C(Naira)) can be extended to be a real linearly isometric map V of E onto C(Naira). From this result we also obtain some corollaries. This is the first time we study this problem on different typical spaces, and the method of proof is also very different too.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-003-0240-z