空间lp(Γ)(1 < p < ∞)和Banach空间E的单位球面之间等距算子的延拓

蒋艳, 陈绍雄

数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 687-696.

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数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 687-696. DOI: 10.12386/A2011sxxb0072
论文

空间lp(Γ)(1 < p < ∞)和Banach空间E的单位球面之间等距算子的延拓

    蒋艳1, 陈绍雄2
作者信息 +

Extension of Isometries Between the Unit Spheres of lp(Γ) (1 < p < ∞) and a Banach Space E

    Yan JIANG1, Shao Xiong CHEN2
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摘要

研究了空间lp(Γ)(1 < p < ∞)和Banach空间E的单位球面之间的非满等距映射V0的延拓问题. 我们得到,满足一定条件的V0可线性等距延拓到全空间lp上.  

Abstract

We mainly study linearly extension of isometric mapping V0 between the Unit spheres of lp(Γ) (1 < p < ∞) and a Banach space E. We show that if V0 satisfies some hypotheses, then V0 can be extended to a linear isometry defined on the whole space.  

关键词

Tingley问题 / 等距延拓 / 等距映射

Key words

Tingley’s problem / isometric extension / isometric mapping

引用本文

导出引用
蒋艳, 陈绍雄. 空间lp(Γ)(1 < p < ∞)和Banach空间E的单位球面之间等距算子的延拓. 数学学报, 2011, 54(4): 687-696 https://doi.org/10.12386/A2011sxxb0072
Yan JIANG, Shao Xiong CHEN. Extension of Isometries Between the Unit Spheres of lp(Γ) (1 < p < ∞) and a Banach Space E. Acta Mathematica Sinica, Chinese Series, 2011, 54(4): 687-696 https://doi.org/10.12386/A2011sxxb0072

参考文献

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[3] Ding G. G., The 1-Lipschitz mapping between the unit sphere of two Hilbert space can be extended to a real linear isometry of the whole space, Sci. in China, Ser. A, 2002, 45(4): 476-483.

[4] Liu R., The 1-Lipschitz mapping of the unit sphere on Banach spaces, Acta Mathematica Sinica, Chinese Series, 2007, 50(5): 1063-1067.

[5] Fang X. N., Wang J. H., On extension of isometries between the unit sphere of normed space E and C(Ω), Acta Mathematica Sinica, English Series, 2006, 22(6): 1819-1824.

[6] An G. M., The isometric extension of the unit spheres, Acta Mathematica Sinica, Chinese Series, 2004, 47(4): 653-656.

[7] Ding G. G., The isometric extension problem in the unit sphere of lp(Γ) (p > 1) type spaces, Science in China, 2002, 32(11): 991-995 (in Chinese); 2003, 46(3): 333-338 (in English).

[8] Ding G. G., The representation theorem of onto isomeric mapping between two unit sphere of l1(Γ) type space and the application on isometric extension problem, Acta Mathematica Sinica, English Series, 2004, 20(6): 1089-1094.

[9] Fang X. N., On extension of 1-Lipschitz mapping between two uint sphere of lp(Γ) type space (1 < p < ∞), Journal of mathematical Research & Exposition, 2009, 29(4): 687-692.

[10] Fang X. N., Wang J. H., On extension of isometries between the unit sphere of normed space E and lp(Γ), Acta Mathematica Sinica, Chinese Series, 2008, 51(1): 23-28.

[11] Ding G. G., The isometric extension of an into mapping from the uint sphere S(l(Γ)) to the unit sphere S(E), Acta Math. Scientia, 2009, 29(B)(3): 469-479.

[12] Ding G. G., The isometric extension of the unit sphere on AL-space, Science in China, Ser. A, 2008, 38(5): 541-555.

[13] Yi J. J., Wang R. D., On Extension of isometries Between the Unit Spheres of Normed Space E and lp (p > 1), Mathematica Sinica, English Series, 2009, 25(7): 1139-1144.

[14] Fang X. N., Wang J. H., Extension of isometries on the unit sphere of lp(Γ) space, Science China. Mathematics, 2010, 53(4): 1085-1096.

基金

云南省社会发展科技计划基础研究面上项目(2009CD042)

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