两个同类的E(2)型空间线性等距映射的表现定理

Abstract

Abstract:

In this paper, the authors give a representation of surjective isometries between the unit spheres of E₍₂₎ type real space if these isometries can be extended to be real linear isometries on the whole space.

Key words: Isometry, Representation, E₍₂₎ space

CLC Number:

46B20

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LIANG Xiao-Bin, HUANG Shi-Xiang. On the Representation |of Linear Isometries between E₍₂₎ Type Real Space[J].Acta mathematica scientia,Series A, 2010, 30(4): 1088-1093.

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References

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[4] Ding Guanggui. The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space. Science in China (Ser A), 2002, 45: 479--483

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[6] Banach. Theori\v{e} des Op\v{e}rations Lin\v{e}airs. Warszawa: Monografie Matematyczne, 1932

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On the Representation |of Linear Isometries between E(2) Type Real Space

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