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Isometries and additive mapping on the unit spheres of normed spaces
- Source :
- Acta Mathematica Sinica, English Series. 33:1431-1442
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
Abstract
- In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.
- Subjects :
- Unit sphere
Pure mathematics
Applied Mathematics
General Mathematics
010102 general mathematics
Mathematical analysis
010103 numerical & computational mathematics
Extension (predicate logic)
01 natural sciences
Domain (mathematical analysis)
Additive function
Isometry
Mathematics::Metric Geometry
SPHERES
0101 mathematics
Unit (ring theory)
Normed vector space
Mathematics
Subjects
Details
- ISSN :
- 14397617 and 14398516
- Volume :
- 33
- Database :
- OpenAIRE
- Journal :
- Acta Mathematica Sinica, English Series
- Accession number :
- edsair.doi...........d2ff075385f71b1c93120909d82a15d8