近似保正交线性映射的扰动  

Perturbations of Approximate Orthogonality Preserving Mapping

作　　者：孔亮[1] 

机构地区：[1]商洛学院应用数学研究所,陕西商洛726000

出　　处：《海南大学学报（自然科学版）》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)

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.

关 键 词：扰动 近似正交 近似等距 近似保正交映射 

分 类 号：O177.1[理学—数学]