广义框架的不相交性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (3): 589-596.

广义框架的不相交性

张伟^1,*(),李云章²()

¹ 河南财经政法大学数学与信息科学学院郑州 450046
² 北京工业大学应用数理学院北京 100124

收稿日期:2019-05-24 出版日期:2020-06-26 发布日期:2020-07-15
通讯作者: 张伟 E-mail:zwfylhappy@126.com;yzlee@bjut.edu.cn
作者简介:李云章, E-mail:yzlee@bjut.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)

Disjointness of Generalized Frames

Wei Zhang^1,*(),Yunzhang Li²()

¹ School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046
² College of Applied Sciences, Beijing University of Technology, Beijing 100124

Received:2019-05-24 Online:2020-06-26 Published:2020-07-15
Contact: Wei Zhang E-mail:zwfylhappy@126.com;yzlee@bjut.edu.cn
Supported by:
the NSFC(11761079);the MPHE of Henan Province(20A110013)

摘要/Abstract

摘要：

Hilbert空间中框架的不相交性是由Han和Larson首先提出的，它与超框架有着密切的联系，在超框架及框架的构造中扮演重要的角色.广义框架是通常框架的推广.该文利用超广义框架刻画了广义框架的不相交性、强不相交性及弱不相交性；借助所得结果，给出了已知定理的不同证明方法；建立了对偶广义框架之间强不相交相和弱不相交性之间的关系；最后利用给定的强不相交的广义框架构造新的（超）对偶广义框架，所得结论恢复已有结果.

关键词: 广义框架, 对偶广义框架, 不相交性

Abstract:

The notion of disjointness of frames in Hilbert spaces was firstly introduced by Han and Larson, it is closely related with super frames in Hilbert spaces, and plays an important role in construction of super frames and frames. G-frames is a generalization of frames in Hilbert spaces. In this paper, we establish characterization of disjointness of g-frames, strong disjointness of g-frames and weak disjointness of g-frames in terms of super g-frames; With the results obtained, we give different proof method of the known theorem; We obtain the relation between strongly disjoint and weakly disjoint of dual g-frames; Finally, we use strong disjointness of g-frames to construct (super) dual g-frames, which cover the results obtained by other authors.

Key words: Generalized frames, Dual generalized frame, Disjointness

中图分类号:

O174.2

张伟,李云章. 广义框架的不相交性[J]. 数学物理学报, 2020, 40(3): 589-596.

Wei Zhang,Yunzhang Li. Disjointness of Generalized Frames[J]. Acta mathematica scientia,Series A, 2020, 40(3): 589-596.

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