K-框架和紧K-框架的算子扰动的稳定性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 29-38.

K-框架和紧K-框架的算子扰动的稳定性

杜丹丹(),朱玉灿*()

福州大学数学与计算机科学学院福州 350116

收稿日期:2019-10-08 出版日期:2021-02-26 发布日期:2021-01-29
通讯作者: 朱玉灿 E-mail:1277702125@qq.com;zhuyucan@fzu.edu.cn
作者简介:杜丹丹, E-mail: 1277702125@qq.com
基金资助:
福建省自然科学基金(2016J01014);福建省自然科学基金(2020J01496)

Stabilities of K- Frames and Tight K- Frames Under the Operator Perturbation

Dandan Du(),Yucan Zhu*()

College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116

Received:2019-10-08 Online:2021-02-26 Published:2021-01-29
Contact: Yucan Zhu E-mail:1277702125@qq.com;zhuyucan@fzu.edu.cn
Supported by:
Supported by the Natural Science Foundation of Fujian Province(2016J01014);Supported by the Natural Science Foundation of Fujian Province(2020J01496)

摘要/Abstract

摘要：

该文在Hilbert空间中讨论K-框架和紧K-框架在算子扰动中的稳定性.首先给出K-框架经过有界线性算子 $T $扰动后为K-框架的充要条件，其次讨论了用两个Bessel序列或者两个K-框架构造新的K-框架的方法，最后给出用两个Bessel序列构造紧K-框架的充要条件.这些结果推广和改进了由Christensen和Casazza等得到的著名结果.

关键词: K-框架, 紧K-框架, Bessel序列, 稳定性

Abstract:

In this paper, we discuss the stabilities of K-frames and tight K-frames under the operator perturbation. Firstly, we provide an equivalent characterization of the operator perturbation for a K-frame by using a bounded linear operator $T $ from ${{\cal H}_1} $ to ${{\cal H}_2} $. We also give a simple way to construct new K-frames from two existing Bessel sequences. Meanwhile, we make a discussion on the construction for K-frames from given ones. In the end, we obtain a necessary and sufficient condition to generate tight K-frames from two old Bessel sequences. Our results generalize and improve the remarkable results which had been obtained by Casazza and Christensen.

Key words: K- frame, Tight K- frame, Bessel sequence, Stability

中图分类号:

O171.1

杜丹丹,朱玉灿. K-框架和紧K-框架的算子扰动的稳定性[J]. 数学物理学报, 2021, 41(1): 29-38.

Dandan Du,Yucan Zhu. Stabilities of K- Frames and Tight K- Frames Under the Operator Perturbation[J]. Acta mathematica scientia,Series A, 2021, 41(1): 29-38.

参考文献 16

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