Hilbert直和空间中g-Riesz基的性质及扰动  

Properties and Perturbations of g-Riesz Basis in Hilbert Direct Sum Spaces

作　　者：申鹏 张建平 张磊 SHEN Peng;ZHANG Jian-ping;ZHANG Lei(School 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：《数学的实践与认识》2023年第9期191-200,共10页Mathematics in Practice and Theory

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

摘　　要：g-框架作为Hilbert空间中传统框架的推广,有着许多与传统框架相似的性质.本文把g-Riesz基的一些性质推广到Hilbert直和空间中,证明了两个g-Riesz基的直和是它们直和空间上的g-Riesz基,并得到了g-Riesz基的直和在其框架逆算子作用下仍然是它们直和空间上的g-Riesz基;最后借助g-Bessel序列的性质讨论了g-Riesz基的扰动.As a generalization of traditional frames in Hilbert spaces,g-frames have many properties similar to traditional frames.In this paper,we generalize some properties of g-Riesz bases to Hilbert direct sum spaces,prove that the direct sum of two g-Riesz bases is g-Riesz bases on their direct sum spaces,and obtain that the direct sum of g-Riesz bases is still g-Riesz bases on their direct sum spaces under the action of its frame inverse operator;Finally,the perturbation of g-Riesz basis is discussed by using the properties of g-Bessel sequence.

关 键 词：G-框架 g-Riesz基 g-Bessel序列 预框架算子 扰动 

分 类 号：O177[理学—数学]