Hilbert空间中广义框架的Q-(近似)对偶

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 694-704.

Hilbert空间中广义框架的Q-(近似)对偶

张伟^1,*(),付艳玲²(),李拴保³()

¹ 河南财经政法大学数学与信息科学学院郑州 450046
² 河南财政金融学院统计与数学学院郑州 450046
³ 河南财政金融学院人工智能学院郑州 450046

收稿日期:2021-05-19 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 张伟 E-mail:zwfylhappy@126.com;jzhou111@163.com;phdfuli@whu.edu.cn
作者简介:付艳玲, E-mail: jzhou111@163.com|李拴保, E-mail: phdfuli@whu.edu.cn
基金资助:
国家自然科学基金(11761079);河南省高等学校重点科研项目(20A110013);河南省高等学校重点科研项目(21A110004);河南省科技攻关项目(182102210215);河南省科技攻关项目(222102210335)

Q-(Approximate) Dual of g-Frames in Hilbert Spaces

Wei Zhang^1,*(),Yanling Fu²(),Shuanbao Li³()

¹ School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046
² School of Statistics and Mathematics, Henan Finance University, Zhengzhou 450046
³ School of Artificial Intelligence, Henan Finance University, Zhengzhou 450046

Received:2021-05-19 Online:2022-06-26 Published:2022-05-09
Contact: Wei Zhang E-mail:zwfylhappy@126.com;jzhou111@163.com;phdfuli@whu.edu.cn
Supported by:
the NSFC(11761079);the Key Scientific Research Projects of Colleges and Universities of Henan Province(20A110013);the Key Scientific Research Projects of Colleges and Universities of Henan Province(21A110004);the Science and Technology Research Project of Henan Province(182102210215);the Science and Technology Research Project of Henan Province(222102210335)

摘要/Abstract

摘要：

该文融合Fusion对偶框架与近似对偶广义框架的思想, 给出了Q-(近似)对偶广义框架的概念, 讨论了Q-近似对偶广义框架与Q-对偶之间的关系, 得到了Q-(近似)对偶广义框架的刻画. 最后, 借助Q-近似对偶广义框架, 给出了一广义框架接近另一广义框架的若干等价条件.

关键词: 广义框架, Q-(近似)对偶广义框架, 接近

Abstract:

In this paper, fusing the ideas of dual Fusion frames and approximate dual g-frames, the definitions of Q-(approximate) dual g-frames are given. The relationship between Q-approximate dual g-frames and Q-dual g-frames is discussed. The characterizations of Q-(approximate) dual g-frames are obtained. Finally, by means of Q-approximate dual g-frames, some equivalent conditions for a g-frame to be close to another g-frame are given.

Key words: G-frame, Q-(approximate) dual g-frame, Closeness

中图分类号:

O174.2

张伟,付艳玲,李拴保. Hilbert空间中广义框架的Q-(近似)对偶[J]. 数学物理学报, 2022, 42(3): 694-704.

Wei Zhang,Yanling Fu,Shuanbao Li. Q-(Approximate) Dual of g-Frames in Hilbert Spaces[J]. Acta mathematica scientia,Series A, 2022, 42(3): 694-704.

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