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近似保正交线性映射的扰动 被引量：1

Perturbations of Approximate Orthogonality Preserving Mapping
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摘要 在复Hilbert空间中,给出了近似等距的定义,给出了近似保正交线性映射的一个充分条件,得到了近似保正交线性映射的扰动定理,即证明了在一定条件下,近似保正交线性映射与近似等距的和或积是近似保正交线性映射. In complex Hilbert spaces,the definition of an approximate isometry was proposed,a sufficient condition for a linear mapping to be an approximate orthogonality preserving mapping was also proposed. The perturbations of an approximate orthogonality preserving linear mapping were obtained. Under certain conditions,it was proved that the sum or composition of an approximate orthonality preserving mapping and an almost isometry is an approximate orthonality preserving mapping.
作者 孔亮
机构地区 商洛学院应用数学研究所
出处 《海南大学学报（自然科学版）》 CAS 2015年第2期115-119,共5页 Natural Science Journal of Hainan University
基金 陕西省科技厅科研项目(2012JM1018) 陕西省教育厅科研项目(2013JK0570) 商洛学院科研项目(14SKY016)
关键词 扰动 近似正交 近似等距 近似保正交映射 perturbation approximate orthogonality almost isometry approximate orthogonality preserving mapping
分类号 O177.1 [理学—基础数学]
  • 相关文献

参考文献18

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共引文献19

同被引文献12

  • 1Chmieliński J.Linear mappings approximately preserving orthogonality[J].J Math Anal Appl,2005,301(1):158-169.
  • 2Chmieliński J.Stability of the orthogonality preserving property in finite-dimensional inner product spaces[J].J Math Anal Appl,2006,318(2):433-443.
  • 3Blanco A,Turn?ek A.On maps that preserve orthogonality in normed spaces[J].Proc Roy Soc Edinburgh Sect A,2006,136(4):709-716.
  • 4Turn?ek A.On mappings approximately preserving orthogonality[J].J Math Anal Appl,2007,336(1):625-631.
  • 5Ili?evic D,Turn?ek A.Approximately orthogonality preserving mappings on C*-modules[J].J Math Anal Appl,2006,318(2):433-443.
  • 6Chmieliński J,Wójcik P.Isosceles-orthogonality preserving property and its stability[J].Nonlinear Anal,2010,72(8):1445-1453.
  • 7Moj?kerc B,Turn?ek A.Mapping approximately preserving orthogonality in normed spaces[J].Nonlinear Anal,2010,73(12):3821-3831.
  • 8Burgos M.Orthogonality preserving linear maps on C*-algebras with non-zero socles[J].J Math Anal Appl,2013,401(2):479-487.
  • 9Cazassa P G,Christensen O.Perturbation of operators and applications to frame theory[J].J Fourier Anal Appl,1997,3(5):543-557.
  • 10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. 被引量：13

引证文献1

海南大学学报（自然科学版）
2015年 第2期

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