关于g-框架与交错对偶g-框架稳定性的研究  

Study on stability of g-frames and alternating dual g-frames

作　　者：张艳 张建平 ZHANG Yan;ZHANG Jianping(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2022年第4期83-88,共6页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学基金项目(11961072);陕西省自然科学基础研究计划项目(2020JM-547)。

摘　　要：Hilbert空间中的g-框架是框架的推广,具有很好的性质。从泛函分析的角度,用算子论的方法通过余等距算子、有界算子、满射算子与g-框架相结合,给出g-框架在算子扰动下仍为g-框架的几个结果;引入Hilbert空间中交错对偶g-框架的概念并讨论与其相关的一些性质,给出两个g-Bessel序列成为交错对偶g-框架的充要条件,证明了互为交错对偶的两个g-框架的和是g-框架,并给出互为交错对偶的两个g-框架分别在可逆算子作用下仍互为交错对偶g-框架的充要条件。g-frame in Hilbert space is a generalization of frame and has good properties. From the perspective of functional analysis,this paper combines g-frame with remainder isometric operator,bounded operator,surjective operator of operator theory,and gives some results that show that g-frame is still g-frame under operator perturbation. This paper introduces the definition of alternating dual g-frames in Hilbert space and discusses some properties related to it. The necessary and sufficient conditions are given for two g-Bessel sequences to become alternating dual g-frames,and the sum of two g-frames which are alternating dual to each other is proved to be a g-frame. The necessary and sufficient conditions are given for two g-frames which are alternating dual to each other to remain alternating dual g-frames under the action of invertible operators respectively.

关 键 词：G-框架 交错对偶g-框架 稳定性 算子论 

分 类 号：O777.1[理学—晶体学]