On isometric extension problem between two unit spheres 被引量：12

On isometric extension problem between two unit spheres

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摘要 In this paper we introduce the isometric extension problem of isometric mappings between two unit spheres. Some important results of the related problems are outlined and the recent progress is mentioned. In this paper we introduce the isometric extension problem of isometric mappings between two unit spheres. Some important results of the related problems are outlined and the recent progress is mentioned.

作者 Ding GuangGui School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

出处《Science China Mathematics》 SCIE 2009年第10期2069-2083,共15页 中国科学：数学（英文版）

基金 supported by Research Foundation for Doctor Programme (Grant No. 20060055010) National Natural Science Foundation of China (Grant No. 10871101)

关键词 normed space isometric extension isometric mapping 1-Lipschitz mapping 46A22 46B02 46B04 46B20 46B22 normed space isometric extension isometric mapping 1-Lipschitz mapping

分类号 O177 [理学—基础数学]

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参考文献5

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二级参考文献9

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共引文献77

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
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
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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49

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
4FANG 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
5CHENG LiXin, SHI HuiHua & ZHANG Wen School of Mathematical Sciences, Xiamen University, Xiamen 361005, China.Every Banach space with a w*-separable dual hasa 1+ε-equivalent norm with the ball covering property[J].Science China Mathematics,2009,52(9):1869-1874. 被引量：6
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
7CHENG LiXin,CHENG QingJin,LIU XiaoYan.Ball-covering property of Banach spaces that is not preserved under linear isomorphisms[J].Science China Mathematics,2008,51(1):143-147. 被引量：12
8马玉梅.ISOMETRIES OF THE UNITE SPHERE[J].Acta Mathematica Scientia,1992,12(4):366-373. 被引量：4
9Guang Gui DING.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[J].Acta Mathematica Sinica,English Series,2004,20(6):1089-1094. 被引量：30
10傅瑞瑜,程立新.Banach空间单位球面的球覆盖性质[J].数学研究,2006,39(1):39-43. 被引量：12

引证文献12

1FANG 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
2陈绍雄,黄中杰.空间L^p(Γ,Σ,μ)(1<p<∞)和Banach空间E的单位球面之间等距算子的延拓[J].云南师范大学学报（自然科学版）,2012,32(2):8-15.
3Dong Ni TAN.Extension of Isometries on the Unit Sphere of L^p Spaces[J].Acta Mathematica Sinica,English Series,2012,28(6):1197-1208. 被引量：3
4李建泽.某类F-空间单位球面上的等距映射(英文)[J].南开大学学报（自然科学版）,2012,45(2):80-85. 被引量：1
5Ryotaro TANAKA.Tingley's Problem on Symmetric Absolute Normalized Norms on R^2[J].Acta Mathematica Sinica,English Series,2014,30(8):1324-1340. 被引量：5
6伊继金,王瑞东,王晓晓.EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX lp(Γ)(p > 1) SPACES[J].Acta Mathematica Scientia,2014,34(5):1540-1550. 被引量：3
7Rui Dong WANG,Xu Jian HUANG.Isometries and Additive Mapping on the Unit Spheres of Normed Spaces[J].Acta Mathematica Sinica,English Series,2017,33(10):1431-1442. 被引量：3
8Guang Gui DING,Jian Ze LI.Isometric Extension Problem Between Strictly Convex Two-dimensional Normed Spaces[J].Acta Mathematica Sinica,English Series,2019,35(4):513-518.
9程立新.Banach空间的保度量(等距)映射[J].中国科学：数学,2020,50(12):1667-1694.
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二级引证文献16

1定光桂.关于Banach空间单位球面间的等距延拓问题[J].数学物理学报（A辑）,2010,30(5):1198-1209. 被引量：1
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5胡锐.L^p空间单位球面上的等距线性延拓[J].数学物理学报（A辑）,2012,32(3):510-520. 被引量：1
6王瑞东,王普.b^(2)空间及b^(2)空间上的等距映射[J].数学学报（中文版）,2019,62(2):303-318.
7定光桂.等距线性延拓问题[J].中国科学：数学,2015,45(1):1-8. 被引量：5
8Guang 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
9刘晓伟.二维赋范空间单位球面间的等距映射的线性延拓[J].山东大学学报（理学版）,2017,52(2):44-48.
10梁晓斌.F_((3))型空间的线性等距映射[J].数学进展,2017,46(3):424-428.

1Guang 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
2GUAN Qi'An,ZHOU Xiang Yu.Optimal constant in an L^2 extension problem and a proof of a conjecture of Ohsawa[J].Science China Mathematics,2015,58(1):35-59. 被引量：8
3Guang Gui DING.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[J].Acta Mathematica Sinica,English Series,2004,20(6):1089-1094. 被引量：30
4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
5张秀英,王宇.(Right)Partial Generalized Automorphisms of Semiprime Rings[J].Northeastern Mathematical Journal,2002,18(3):261-265.
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
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
8Xiao Hong FU Department of Mathematics,Jiaying College,Meizhou 514015,P.R.China.The Isometric Extension of the Into Mapping from the Unit Sphere S_1(E) to S_1(l~∞(Г))[J].Acta Mathematica Sinica,English Series,2008,24(9):1475-1482. 被引量：8
9定光桂.THE ISOMETRIC EXTENSION OF AN INTO MAPPING FROM THE UNIT SPHERE S[e(Γ)] TO THE UNIT SPHERE S(E)[J].Acta Mathematica Scientia,2009,29(3):469-479. 被引量：6
10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

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