| 连续型K-g-框架的一些构造方法 |
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| 引用本文： | 余 鑫,林丽琼.连续型K-g-框架的一些构造方法[J].福州大学学报(自然科学版),2023,51(4):439-444. |
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| 作者姓名： | 余 鑫 林丽琼 |
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| 作者单位： | 福州大学数学与统计学院,福州大学数学与统计学院 |
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| 基金项目： | 福建省自然科学基金资助项目（面上项目，重点项目，重大项目） |
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| 摘 要： | 本文给出连续型(紧)K-g-框架的若干构造方法. 事实上, 本文利用正算子给出连续型K1-g-框架与连续型g-Bessel族(连续型K1-g-框架)的算子摄动的和成为连续型K2-g-框架的充分条件, 给出连续型K1-g-框架的算子摄动成为连续型K2-g-框架的充要条件. 本文也给出两个连续型g-Bessel族的算子摄动的和成为连续型紧K-g-框架的充要条件.
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| 关 键 词： | Hilbert空间 连续型K-g-框架 连续型紧K-g-框架 连续型g-Bessel族 |
| 收稿时间： | 2022/4/16 0:00:00 |
| 修稿时间： | 2022/6/2 0:00:00 |
Some construction methods of continuous K-g-frames |
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| YU Xin,LIN Liqiong.Some construction methods of continuous K-g-frames[J].Journal of Fuzhou University(Natural Science Edition),2023,51(4):439-444. |
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| Authors: | YU Xin LIN Liqiong |
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| Institution: | School of Mathematics and Statistics, Fuzhou University,School of Mathematics and Statistics, Fuzhou University |
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| Abstract: | In this paper, some construction methods of continuous (compact) K-g-frames are given. In fact, this paper gives some sufficient conditions for the sum of the operator perturbations of a continuous K1-g-frame and a continuous g-Bessel family (or a continuous K1-g-frame) becoming a continuous K2-g-frame. It gives a necessary and sufficient conditions for the operator perturbations of a continuous K1-g-frame becoming a continuous K2-g-frame. This paper also gives a necessary and sufficient condition for the sum of operator perturbations of two continuous g-Bessel families becoming a continuous compact K-g-frame. |
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| Keywords: | Hilbert Spaces continuous K-g-frames continuous tight K-g-frames continuous g-Bessel families |
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