Q-duals and Q-approximate duals of g-frames in Hilbert spaces

被引：1
|
作者：
Xiao, Xiangchun [1 ,2 ]
Zhao, Guoping [1 ]
Zhou, Guorong [1 ]
机构：
[1] Xiamen Univ Technol, Sch Math & Stat, Xiamen, Peoples R China
[2] Xiamen Univ Technol, Sch Math & Stat, Xiamen 361024, Peoples R China
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2023年 / 44卷 / 06期
关键词：
Approximate dual; G-frame; Q-dual; synthesis operator; FUSION FRAMES; STABILITY;
D O I：
10.1080/01630563.2023.2184383
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we mainly discuss the properties of Q-duals and Q-approximate duals of g-frames in Hilbert spaces. Given {boolean AND(j)}(j is an element of J) and {theta(j)}(j is an element of J) being a pair of Q-dual, {gamma(j)}(j is an element of J) being some kind of perturbed sequence of {theta(j)}(j is an element of J), in general {boolean AND(j)}(j is an element of J) is not a Q-approximate dual of {gamma(j)}(j is an element of J) . We then give four differ-ent kinds of perturbed conditions such that {boolean AND(j)}(j is an element of J) and {gamma(j)}(j is an element of J), a perturbed sequence of {theta(j)}(j is an element of J), are possible to be a pair of Q-approximate dual. We also provide several different methods to construct Q-duals and Q-approximate duals of g-frames. Finally, we give two equivalent characterizations of Q- duals and Q-approximate duals by using the associated induced sequences.
引用
收藏
页码：510 / 528
页数：19
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