数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1540-1550.doi: 10.1016/S0252-9602(14)60102-8

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EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX l p(Γ)(p >|1) SPACES

伊继金|王瑞东|王晓晓   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China; Department of Mathematics, Tianjin University of Technology, Tianjin 300191, China; School of Foreign Language Education, Liaocheng University, Liaocheng 252059, China
  • 收稿日期:2013-02-27 修回日期:2013-12-12 出版日期:2014-09-20 发布日期:2014-09-20
  • 基金资助:

    The first author is supported by Higher Educa-tional Science and Technology Program Foundation of Shandong Province (J11LA02), Young and Middle-Aged Scientists Research Foundation of Shandong Province (BS2010SF004) and Higher Educational Science and Tech-nology Program Foundation of Shandong Province (J10LA53).

EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX l p(Γ)(p >|1) SPACES

 YI Ji-Jin, WANG Rui-Dong, WANG Xiao-Xiao   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China; Department of Mathematics, Tianjin University of Technology, Tianjin 300191, China; School of Foreign Language Education, Liaocheng University, Liaocheng 252059, China
  • Received:2013-02-27 Revised:2013-12-12 Online:2014-09-20 Published:2014-09-20
  • Supported by:

    The first author is supported by Higher Educa-tional Science and Technology Program Foundation of Shandong Province (J11LA02), Young and Middle-Aged Scientists Research Foundation of Shandong Province (BS2010SF004) and Higher Educational Science and Tech-nology Program Foundation of Shandong Province (J10LA53).

摘要:

In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces l p(Γ) and l p(Δ)(p > 1). We first derive the representation of isometries between the unit spheres of complex Banach spaces l p(Γ) and l p(Δ). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces l p(Γ)and l p(Δ) can be extended to be a linear isometry on the whole space.

关键词: isometric mapping, isometric extension, strictly convex

Abstract:

In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces l p(Γ) and l p(Δ)(p > 1). We first derive the representation of isometries between the unit spheres of complex Banach spaces l p(Γ) and l p(Δ). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces l p(Γ)and l p(Δ) can be extended to be a linear isometry on the whole space.

Key words: isometric mapping, isometric extension, strictly convex

中图分类号: 

  • 46B04