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.
作者
杜丹丹
朱玉灿
Du Dandan;Zhu Yucan(College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350116)
出处
《数学物理学报（A辑）》
CSCD
北大核心
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)。
