您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (06): 75-82.doi: 10.6040/j.issn.1671-9352.0.2014.571

• 论文 • 上一篇    下一篇

ε-近似保平方等腰正交映射的刻画与扰动

孔亮1, 曹怀信2   

  1. 1. 商洛学院应用数学研究所, 陕西 商洛 726000;
    2. 陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 收稿日期:2014-12-22 修回日期:2015-04-21 出版日期:2015-06-20 发布日期:2015-07-31
  • 作者简介:孔亮(1983-),男,硕士,讲师,研究方向为算子理论.E-mail:kongliang2005@163.com
  • 基金资助:
    国家自然科学基金资助项目(11371012)

Characterization and perturbations of ε-approximate square isosceles-orthogonality preserving mappings

KONG Liang1, CAO Huai-xin2   

  1. 1. Institute of Applied Mathematics, Shangluo University, Shangluo 726000, Shaanxi, China;
    2. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
  • Received:2014-12-22 Revised:2015-04-21 Online:2015-06-20 Published:2015-07-31

PDF (PC)

658

摘要： 在实赋范线性空间中, 给出了ε-近似保平方等腰正交映射的定义, 得到了ε-近似保平方等腰正交线性映射的一些充分条件, 在映射有界的条件下, 给出了ε-近似保平方等腰正交线性映射的刻画, 最后得到了ε-近似保平方等腰正交线性映射的扰动定理。

关键词: -近似等距, &epsilon, -近似平方等腰正交, &epsilon, -近似保平方等腰正交映射, 等腰正交, &delta

Abstract: Firstly, In real normed linear spaces, the definition of ε-approximate square isosceles-orthogonality preserving mapping is given. Some sufficient conditions for a linear mapping to be an ε-approximate square isosceles-orthogonality preserving mapping are given. Secondly, when the mapping is bounded, the characterization of ε-approximate square isosceles-orthogonality preserving linear mapping is obtained. Finally, the perturbations of ε-approximate square isosceles-orthogonality preserving linear mapping are given.

Key words: ε-approximate square isosceles-orthogonality, δ-approximate isometry, isosceles-orthogonality, ε-approximate square isosceles-orthogonality preserving mapping

中图分类号: 

  • O177.1
[1] ROBERTS B D. On the geometry of abstract vector space[J]. Thoku Math J, 1934, 39:42-59.
[2] BIRKHOFF G. Orthogonality in linear metric space[J]. Duke Math J, 1935, 1(2):169-172.
[3] JAMES R C. Orthogonality in normed linear space[J]. Duke Math J, 1945, 12(2):291-302.
[4] FATHI B S. An extension of the notion of orthogonality to Banach spaces[J]. J Math Anal Appl, 2002, 267(1):29-47.
[5] 付向红, 黎永锦. Banach空间的非常B-正交性[J]. 中山大学学报:自然科学版, 2008, 47(1):116-117. FU Xianghong, LI Yongjin. The very B-orthogonality in Banach space[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2008, 47(1):116-117.
[6] 杨冲, 张登华. Banach空间中Birkhoff正交性的刻画[J]. 数学的实践与认识, 2008, 38(9):187-192. YANG Chong, ZHANG Denghua. Characterizations of Birkhoff orthogonality in Banach space[J]. Journal of Mathematics in Practice and Theory, 2008, 38(9):187-192.
[7] DING G G. Isometric and almost isometric operator[J]. Acta Math Sci, 1984, 4(2):221-226.
[8] CHMIELI?SKI J. Linear mappings approximately preserving orthogonality[J]. J Math Anal Appl, 2005, 304(1):158-169.
[9] CHMIELI?SKI J. Stability of the orthogonality preserving property in finite-dimensional inner product spaces[J]. J Math Anal Appl, 2006, 318(2):433-443.
[10] BLANCO A, TURNŠEK A. On maps that preserve orthogonality in normed spaces[J]. Trans Proc Roy Soc Edinburgh: Sect A, 2006, 136(4):709-716.
[11] TURNŠEK A. On mappings approximately preserving orthogonality[J]. J Math Anal Appl, 2007, 336(1):625-631.
[12] CHMIELI?SKI J. Remarks on orthogonality preserving mappings in normed spaces and some stability problems[J]. Banach J Math Anal, 2007, 1(1):117-124.
[13] 孔亮, 曹怀信. 保正交映射与正交性方程的稳定性[J]. 陕西师范大学学报:自然科学版, 2008, 36(5):10-14. KONG Liang, CAO Huaixin. Stability of orthogonality preserving mappings and the orthogonality equaion[J]. Journal of Shaanxi Normal University: Natural Science Editon, 2008, 36(5):10-14.
[14] ILIŠEVIX D, TURNŠEK A. Approximately orthogonality preserving mappings on C*-modules[J]. J Math Anal Appl, 2008, 341(1):298-308.
[15] 孔亮, 曹怀信. ε-近似保正交映射的稳定性与扰动[J]. 数学学报:中文版, 2010, 53(1):61-66. KONG Liang, CAO Huaixin. ε-Approximate orthogonality preserving mappings[J]. Acta Mathematica Sinica: Chinese Series, 2010, 53(1):61-66.
[16] CHMIELI?SKI J, WÓJCIK P. Isosceles-orthogonality preserving property and its stability[J]. Nonlinear Anal, 2010, 72(3):1445-1453.
[17] 崔建莲, 候晋川. C*代数上保持不定正交性的线性映射[J]. 数学年刊, 2004, 25A(4):437-443. CUI Jianlian, HOU Jinchuan. Linear maps preserving indefinite orthogonality on C*-algebras[J]. Chinese Annal of Mathematics, 2004, 25A(4):437-443.
[18] 张芳娟, 吉国兴. B(H)上保正交性的可加映射[J]. 陕西师范大学学报:自然科学版, 2005, 33(4):21-25. ZHANG Fangjuan, JI Guoxing. Additive maps preserving orthogonality on B(H)[J]. Journal of Shaanxi Normal University:Natural Science Editon, 2005, 33(4):21-25.
[19] WÓJIK P. Linear mappings preserving ρ-orthogonality[J]. J Math Anal Appl, 2012, 386(1):171-176.
[20] BURGOS M. Orthogonality preserving linear maps on C*-algebras with non-zero socles[J]. J Math Anal Appl, 2013, 401(2):479-487.
[1] 王尧, 张玖琳, 任艳丽. 幂零p.p.-环和幂零Baer环的Ore扩张[J]. 山东大学学报（理学版）, 2015, 50(04): 76-81.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发