Hilbert C*-模中对偶g-框架的稳定性  

Stability of Duals of g-Frames in Hilbert C*-Modules

作　　者：相中启[1] 简辉华[2] 

机构地区：[1]上饶师范学院数学计算机学院 [2]新余学院电气与电子工程学院

出　　处：《湖南师范大学自然科学学报》2015年第2期68-73,共6页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(11271148)

摘　　要：完善了Hilbert C*-模中g-框架的稳定性理论.作为准备工作,给出了Hilbert C*-模中g-框架的一个等价定义,说明交替对偶与典范对偶的差别可以认为是一个可伴算子.然后讨论对偶g-框架的稳定性,证明了如果Hilbert C*-模中两个g-框架彼此接近,则可以找到它们的交替对偶,使之彼此接近.This paper perfects the stability theory of g-frames in Hilbert C^＊-modules. As preparations,an equivalent definition of g-frames in Hilbert C^＊-modules is given and it is showed that the difference between the alternate dual and the canonical dual can be considered as an adjointable operator. Subsequently,the stability of duals of g-frames is discussed,and it is proved that if two g-frames in Hilbert C^＊-modules are close to each other,their alternate duals can be found to make them close to each other as well.

关 键 词：HILBERT C^＊-模 G-框架 对偶g-框架 稳定性 

分 类 号：O177.1[理学—数学]