On sum and stability of g-frames in Hilbert spaces

被引：22

作者：

Li, Dongwei ^{[1
]}

Leng, Jinsong ^{[1
]}

Huang, Tingzhu ^{[1
]}

Sun, Guomin ^{[1
]}

机构：

[1] Univ Elect Sci & Technol China, Sch Math Sci, Beijing, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2018年 / 66卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Frame; g-frame; tight g-frame; stability; OPTIMAL DUAL FRAMES; FUSION FRAMES; PERTURBATION; ERASURES;

D O I：

10.1080/03081087.2017.1364338

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give some new results on sum and stability of g-frames in Hilbert spaces. Since the finite sum of g-frames may not be a g-frame for the Hilbert space, we give a necessary and sufficient condition and some sufficient conditions for the finite sum of g-frames to be a g-frame. We also show that every g-sequence in Hilbert space can be expanded to a tight g-frame by adding a linear bounded operator. Moreover, we obtain some sufficient conditions under which g-frames (and the finite sum of g-frames) are stable under small perturbations.

引用

页码：1578 / 1592

页数：15

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