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ε-近似保平方等腰正交映射的刻画与扰动 被引量：2

Characterization and perturbations of ε-approximate square isosceles-orthogonality preserving mappings
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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。 Firstly, In real normed linear spaces, the definition of e-approximate square isosceles-orthogonality preser- ving mapping is given. Some sufficient conditions for a linear mapping to be an ε--approximate square isosceles-orthogo- nality 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.
作者 孔亮 曹怀信
机构地区 商洛学院应用数学研究所 陕西师范大学数学与信息科学学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2015年第6期75-82,共8页 Journal of Shandong University(Natural Science)
基金 国家自然科学基金资助项目(11371012)
关键词 等腰正交 δ-近似等距 ε-近似平方等腰正交 ε-近似保平方等腰正交映射 isosceles-orthogonality δ-approximate isometry ε--approximate square isosceles-orthogonality ε--approxi-mate square isosceles-orthogonality preserving mapping
分类号 O177.1 [理学—基础数学]
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参考文献20

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二级参考文献44

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共引文献19

同被引文献24

  • 1Roberts B D.On the Geometry of Abstract Vector Space[J].Tohoku Math J,1934,39:42-59.
  • 2Birkhoff G. Orthogonality in Linear Metric Space[J].Duck Math J, 1935,1 (2) : 169-172.
  • 3James R C.Orthogonality in Normed Linear Space[J].Duck Math J, 1945,12(2) :291-302.
  • 4Diminnie C R.A New Orthogonality Relation for Normed Linear Spaces[J].Math Nachr, 1983,114(1) :197-203.
  • 5Alonso J,Soriano M L.On Height Orthogonality in Normed Linear Spaces[J].Roeky Mt J Math, 1999,29(4) :1 167-1 183.
  • 6Saidi F B.An Extension of the Notion of Orthogonality to Banach Spaces[J].J Math Anal Appl,2002,267(1) :29-47.
  • 7Chmielinski J, Wojcik P. On a p orthogonality[J]. Aequationes Math, 2010,80 ( 1 ) : 45-55.
  • 8Alonso J, Martini H, Wu S.On Birkhoff Orthogonality and Isosceles Orthogonality in Normed Linear Spaces[J].Aequationes Math, 2012, 88(1/2) : 153-189.
  • 9Chmieliflski J.Linear Mappings Approximately Preserving Orthogonality[J].J Math Anal Appl,2005,301(1) :158-169.
  • 10Chmieliflski J.Stability of the Orthogonality Preserving Property in Finite-dimensional Inner Product Spaces[J].J Math Anal Appl,2006, 318(2) :433-443.

引证文献2

山东大学学报（理学版）
2015年 第6期

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