数学物理学报(英文版)

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CANNOT ISOMETRICALLY CONTAIN SOME THREE-DIMENSIONAL SUBSPACES#br# OF AM-SPACES

定光桂   

  1. 南开大学数学学院, 天津300071
  • 收稿日期:2005-02-20 修回日期:1900-01-01 出版日期:2007-04-20 发布日期:2007-04-20
  • 通讯作者: 定光桂
  • 基金资助:

    This study is supported by the National Natural Science Foundation of China
    (10571090) and the Research Fund for the Doctoral Program of Higher Education (20060055010)

CANNOT ISOMETRICALLY CONTAIN SOME THREE-DIMENSIONAL SUBSPACES#br# OF AM-SPACES

Ding Guanggui   

  1. School of Mathematical Sciences, Shren Institute of Mathematics and LPMC,
    Nankai University, Tianjin 300071, China
  • Received:2005-02-20 Revised:1900-01-01 Online:2007-04-20 Published:2007-04-20
  • Contact: Ding Guanggui

摘要:

This article presents a novel method to prove that: let E be an AM-space and if dim E≥ 3, then there does not exist any odd subtractive isometric mapping from the unit sphere S(E) into $S[L(\Omega,\mu)]$. In particular, there does not exist any real linear isometry from E into $L(\Omega,\mu)$.

关键词: Isometric mapping, odd and subtractive mapping, AM-space

Abstract:

This article presents a novel method to prove that: let E be an AM-space and if dim E≥ 3, then there does not exist any odd subtractive isometric mapping from the unit sphere S(E) into $S[L(\Omega,\mu)]$. In particular, there does not exist any real linear isometry from E into $L(\Omega,\mu)$.

Key words: Isometric mapping, odd and subtractive mapping, AM-space

中图分类号: 

  • 46B04