The Representation Theorem of onto Isometric Mappings between Two Unit Spheres of l^1(Г) Type Spaces and The Application to the Isometric Extension Problem 被引量：30

The Representation Theorem of onto Isometric Mappings between Two Unit Spheres of l^1(Г) Type Spaces and The Application to the Isometric Extension Problem

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摘要 In this paper,we first derive the representation theorem of onto isometric mappings in theunit spheres of l~1(F) type spaces,and then conclude that such mappings can be extended to the wholespace as real linear isometrics by using a previous result of the author. In this paper,we first derive the representation theorem of onto isometric mappings in theunit spheres of l^1(F) type spaces,and then conclude that such mappings can be extended to the wholespace as real linear isometrics by using a previous result of the author.

作者 Guang Gui DING

机构地区 School of Mathematics Science and LPMC

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第6期1089-1094,共6页 数学学报（英文版）

基金 supported by National Science Foundation of China(19971046) the Doctoral Programme Foundation of Ministry of Education of China

关键词 Isometric mapping Isometric extension Isometric mapping Isometric extension

分类号 O174 [理学—数学]

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参考文献2

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共引文献73

1DING Guanggui.The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem[J].Science China Mathematics,2004,47(5):722-729. 被引量：30
2Ding GuangGui School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China.On isometric extension problem between two unit spheres[J].Science China Mathematics,2009,52(10):2069-2083. 被引量：12
3FANG XiNian 1,& WANG JianHua 2 1 School of Mathematics and Statistics,Nanjing Audit University,Nanjing 210029,China,2 Department of Mathematics,Anhui Normal University,Wuhu 241000,China.Extension of isometries on the unit sphere of l^p (Γ) space[J].Science China Mathematics,2010,53(4):1085-1096. 被引量：10
4DING GuangGui School of Mathematics Science, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China.The isometric extension of “into” mappings on unit spheres of AL-spaces[J].Science China Mathematics,2008,51(10):1904-1918. 被引量：7
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6李磊.单位球面上的等距算子的延拓[J].数学学报（中文版）,2005,48(6):1105-1108. 被引量：1
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10Guang Gui DING.A Note on Linear Extension of Into-Isometries Between Two Unit Spheres of Atomic AL^p-Space （0 〈 p 〈∞）[J].Acta Mathematica Sinica,English Series,2006,22(1):279-282. 被引量：3

同被引文献38

1DING Guanggui.The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem[J].Science China Mathematics,2004,47(5):722-729. 被引量：30
2定光桂.The isometric extension problem in the unit spheres of l^p(Г)(p >1) type spaces[J].Science China Mathematics,2003,46(3):333-338. 被引量：24
3定光桂.The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space[J].Science China Mathematics,2002,45(4):479-483. 被引量：48
4Ding GuangGui School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China.On isometric extension problem between two unit spheres[J].Science China Mathematics,2009,52(10):2069-2083. 被引量：12
5FANG XiNian 1,& WANG JianHua 2 1 School of Mathematics and Statistics,Nanjing Audit University,Nanjing 210029,China,2 Department of Mathematics,Anhui Normal University,Wuhu 241000,China.Extension of isometries on the unit sphere of l^p (Γ) space[J].Science China Mathematics,2010,53(4):1085-1096. 被引量：10
6DING GuangGui School of Mathematics Science, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China.The isometric extension of “into” mappings on unit spheres of AL-spaces[J].Science China Mathematics,2008,51(10):1904-1918. 被引量：7
7王日生.ISOMETRIES BETWEEN THE UNIT SPHERES OF C_0(Ω) TYPE SPACES[J].Acta Mathematica Scientia,1994,14(1):82-89. 被引量：6
8马玉梅.ISOMETRIES OF THE UNITE SPHERE[J].Acta Mathematica Scientia,1992,12(4):366-373. 被引量：4
9方习年,王建华.单位球面间等距映射的线性延拓[J].数学学报（中文版）,2005,48(6):1109-1112. 被引量：2
10张伦.关于有限维l^∞空间单位球面之间等距延拓的一个问题[J].南开大学学报（自然科学版）,2006,39(2):110-112. 被引量：2

引证文献30

1Ding GuangGui School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China.On isometric extension problem between two unit spheres[J].Science China Mathematics,2009,52(10):2069-2083. 被引量：12
2FANG XiNian 1,& WANG JianHua 2 1 School of Mathematics and Statistics,Nanjing Audit University,Nanjing 210029,China,2 Department of Mathematics,Anhui Normal University,Wuhu 241000,China.Extension of isometries on the unit sphere of l^p (Γ) space[J].Science China Mathematics,2010,53(4):1085-1096. 被引量：10
3DING GuangGui School of Mathematics Science, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China.The isometric extension of “into” mappings on unit spheres of AL-spaces[J].Science China Mathematics,2008,51(10):1904-1918. 被引量：7
4Guang Gui DING.A Note on Linear Extension of Into-Isometries Between Two Unit Spheres of Atomic AL^p-Space （0 〈 p 〈∞）[J].Acta Mathematica Sinica,English Series,2006,22(1):279-282. 被引量：3
5Guang Gui DING School of Mathematical Science and LPMC,Nankai University,Tianjin 300071,P.R.China.The Isometric Extension of an Into Mapping from the Unit Sphere S(e_((2))~∞)to S(L^1(μ))[J].Acta Mathematica Sinica,English Series,2006,22(6):1721-1724. 被引量：4
6Xi Nian FANG,Jian Hua WANG.Extension of Isometries Between the Unit Spheres of Normed Space E and C(Ω)[J].Acta Mathematica Sinica,English Series,2006,22(6):1819-1824. 被引量：18
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8方习年,王建华.赋范空间E和l^1(Γ)的单位球面间等距映射的延拓[J].数学学报（中文版）,2008,51(1):23-28. 被引量：4
9定光桂.AL-空间单位球面上的等距算子的延拓[J].中国科学（A辑）,2008,38(5):541-555. 被引量：3
10李磊.单位球面上的等距延拓[J].数学物理学报（A辑）,2008,28(6):997-1001.

二级引证文献43

1Ding GuangGui School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China.On isometric extension problem between two unit spheres[J].Science China Mathematics,2009,52(10):2069-2083. 被引量：12
2FANG XiNian 1,& WANG JianHua 2 1 School of Mathematics and Statistics,Nanjing Audit University,Nanjing 210029,China,2 Department of Mathematics,Anhui Normal University,Wuhu 241000,China.Extension of isometries on the unit sphere of l^p (Γ) space[J].Science China Mathematics,2010,53(4):1085-1096. 被引量：10
3DING GuangGui School of Mathematics Science, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China.The isometric extension of “into” mappings on unit spheres of AL-spaces[J].Science China Mathematics,2008,51(10):1904-1918. 被引量：7
4杨秀忠.单位球面上的等距及(λ，ψ，2)-等距映射的延拓[J].数学学报（中文版）,2006,49(6):1397-1402.
5定光桂.AL-空间单位球面上的等距算子的延拓[J].中国科学（A辑）,2008,38(5):541-555. 被引量：3
6李磊.Tsirelson空间的单位球面上等距算子的延拓(英文)[J].南开大学学报（自然科学版）,2009,42(3):108-112.
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10Guang Gui DING.On Linearly Isometric Extensions for 1-Lipschitz Mappings Between Unit Spheres of ALP-spaces (p>2)[J].Acta Mathematica Sinica,English Series,2010,26(2):331-336. 被引量：4

1Ding GuangGui School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China.On isometric extension problem between two unit spheres[J].Science China Mathematics,2009,52(10):2069-2083. 被引量：12
2Guang Gui DING.The Isometric Extension Problem between Unit Spheres of Two Separable Banach Spaces[J].Acta Mathematica Sinica,English Series,2015,31(12):1872-1878. 被引量：2
3定光桂.The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space[J].Science China Mathematics,2002,45(4):479-483. 被引量：48
4DING GuangGui School of Mathematics Science, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China.The isometric extension of “into” mappings on unit spheres of AL-spaces[J].Science China Mathematics,2008,51(10):1904-1918. 被引量：7
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7Guang Gui DING,Yu Mei MA.How to Recognize Nonexpansive Mappings and Isometric Mappings[J].Acta Mathematica Sinica,English Series,2011,27(10):1959-1966. 被引量：1
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9曹烨,王庆钱.关于新万有引力公式的一些补充研究[J].中国科技纵横,2016,0(3):245-245. 被引量：1
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Acta Mathematica Sinica,English Series

2004年第6期

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