K-框架和紧K-框架的算子扰动的稳定性  

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

作　　者：杜丹丹 朱玉灿[1] Du Dandan;Zhu Yucan(College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350116)

机构地区：[1]福州大学数学与计算机科学学院,福州350116

出　　处：《数学物理学报（A辑）》2021年第1期29-38,共10页Acta Mathematica Scientia

基　　金：福建省自然科学基金(2016J01014,2020J01496)。

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.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 H1 to H2.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.

关 键 词：K-框架 紧K-框架 BESSEL序列 稳定性 

分 类 号：O171.1[理学—数学]