The isometric extension problem in the unit spheres of \(l^p(\Gamma)(p>1)\) type spaces. (English) Zbl 1217.46010
Summary: We first derive the representation theorem of onto isometric mappings in the unit spheres of \(l^p(\Gamma)(p>1)\), \(p\neq 2\) type spaces, and then we conclude that such mappings can be extended to the whole space as real linear isometries by using the previous result of the author.
MSC:
| 46B20 | Geometry and structure of normed linear spaces |
| 46B04 | Isometric theory of Banach spaces |
| 46B25 | Classical Banach spaces in the general theory |
References:
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