Hilbert空间中的g-Besselian框架和拟g-Riesz基

数学物理学报 ›› 2014, Vol. 34 ›› Issue (4): 948-959.

Hilbert空间中的g-Besselian框架和拟g-Riesz基

丁明玲¹, 朱玉灿², 肖祥春², 温永仙¹

1.福建农林大学计算机与信息学院福州 350002;
2.福州大学数学与计算机科学学院福州 |350108

收稿日期:2012-10-25 修回日期:2013-11-30 出版日期:2014-08-25 发布日期:2014-08-25
基金资助:
国家自然科学基金(31171448)、国家天元基金(11226099)、福建省自然科学基金(2012J01005, 2014J01007)、福建省教育厅科技资助项目(JA11100)、福州大学科技发展基金(2012-XQ-29)和福州大学科研启动基金(022410)资助.

g-Besselian Frames and Near g-Riesz Bases in Hilbert Spaces

DING Ming-Ling¹, ZHU Yu-Can², XIAO Xiang-Chun², WEN Yong-Xian¹

1.College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou 350002;
2.Department of Mathematics, Fuzhou University, Fuzhou 350108

Received:2012-10-25 Revised:2013-11-30 Online:2014-08-25 Published:2014-08-25
Supported by:
国家自然科学基金(31171448)、国家天元基金(11226099)、福建省自然科学基金(2012J01005, 2014J01007)、福建省教育厅科技资助项目(JA11100)、福州大学科技发展基金(2012-XQ-29)和福州大学科研启动基金(022410)资助.

摘要/Abstract

摘要：

在Hilbert空间中, g -框架作为框架的推广, 具有许多类似于框架的性质, 但并非所有的结论都类似. 比如Besselian框架等价于拟Riesz基, 但g-Besselian框架与拟g-Riesz基不等价. 该文刻画了g-Besselian框架与拟g-Riesz基在一定条件下的等价关系;
得到g-Besselian框架与拟g-Riesz基的对偶性结论; 并在Hilbert空间中讨论g-Besselian框架与拟g-Riesz基的稳定性.

关键词: g -框架, g-Besselian框架, 拟g-Riesz基, 对偶g -框架, 稳定性

Abstract:

g-frames, as the generalized frames, have many properties similar to those of the frames in Hilbert spaces, but not all the properties are similar. For example, Besselian frames are equivalent to near Riesz bases, but g-Besselian frames are not equivalent to near g-Riesz bases. In this paper, we give an equivalent relation between a g-Besselian frame and a near g-Riesz basis under some conditions, and also have some results on the duality of g-Besselian frames and near g-Riesz bases. Moreover, we discuss the stability of g-Besselian frames and near g-Riesz bases respectively in Hilbert spaces.

Key words: g-frame, g-Besselian frame, Near g-Riesz basis, Canonical dual g-frame, Stability

中图分类号:

42C99

丁明玲, 朱玉灿, 肖祥春, 温永仙. Hilbert空间中的g-Besselian框架和拟g-Riesz基[J]. 数学物理学报, 2014, 34(4): 948-959.

DING Ming-Ling, ZHU Yu-Can, XIAO Xiang-Chun, WEN Yong-Xian. g-Besselian Frames and Near g-Riesz Bases in Hilbert Spaces[J]. Acta mathematica scientia,Series A, 2014, 34(4): 948-959.

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