K-框架及其K-对偶Bessel序列  

K-frames and its K-dual Bessel sequences

作　　者：郭倩平 冷劲松[2] 李厚彪[2] GUO Qianping;LENG Jingsong;LI Houbiao(School of Mathematics and Information Science,Henan University of Economics and Law,Zhengzhou 450046,China;School of Mathematical Science,University of Electronic Science and Technology of China,Chengdu 611731,China)

机构地区：[1]河南财经政法大学数学与信息科学学院,河南郑州450016 [2]电子科技大学数学科学学院,四川成都611731

出　　处：《浙江大学学报（理学版）》2024年第6期718-723,共6页Journal of Zhejiang University（Science Edition）

基　　金：河南省高等学校重点科研项目(25A110009);河南省优秀青年科学基金项目(222300420022);河南财经政法大学校级一般项目(803271).

摘　　要：研究了K-框架及其K-对偶Bessel序列。首先,给出了Bessel序列为K-框架的充要条件,在闭子空间R(K)上借助逼近K-对偶,研究了构造K-框架及其对偶的方法。其次,给出了两个K-框架是逼近K-对偶的充要条件,得到了构造逼近K-对偶的简单方法。最后,基于K-对偶Bessel序列,在R(K)上构造了可与K-框架交换位置的Bessel序列。K-frames and its K-dual Bessel sequences are discussed.The sufficient and necessary condition for a Bessel sequence to be a K-frame is obtained.Then,we research the duality of K-frames in closed subspace R(K),and the ways of constructing the K-frames by using approximate K-dual.In addition,we give the sufficient and necessary condition for two K-frames to be approximate K-dual,and give a simple method to obtain approximate K-dual.

关 键 词：HILBERT空间 K-框架 BESSEL序列 K-对偶Bessel序列 逼近K-对偶 正交投影算子 

分 类 号：O174.2[理学—数学]