连续广义框架的ε-近似  

ε-approximations of continuous generalized frames

作　　者：张伟 ZHANG Wei(School of Mathematics and Information Sciences,Henan University of Economics and Law,Zhengzhou 450046,Henan,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450046

出　　处：《山东大学学报（理学版）》2024年第4期73-80,共8页Journal of Shandong University(Natural Science)

基　　金：河南省高等学校重点科研项目(21A110004);河南省科技攻关项目(242102210049)。

摘　　要：讨论Hilbert空间中连续广义框架理论,引入了连续广义框架的ε-近似、ε-接近的概念,建立二者之间的联系,得到一定条件下连续广义框架ε-近似也是连续广义框架,但有趣的是,紧连续广义框架ε-近似不可能是紧连续广义框架;给定一个连续广义框架的对偶框架及ε-接近,可以找到其ε-接近的一个对偶连续广义框架使得两个对偶框架彼此靠近。This paper addresses the continuous generalized frame theory in Hilbert spaces.We introduce the concepts ofε-approximation,ε-closeness of continuous generalized frames,and establish a link betweenε-approximation andε-closeness.We present that theε-approximations of continuous generalized frames are continuous generalized frames under certain conditions.Interestingly,theε-approximations of tight continuous generalized frames can not be tight continuous generalized frames.Given a dual frame andε-closeness of a continuous generalized frame,one can find a dual continuous generalized frame of itsε-closeness that makes the two dual continuous generalized frames close to each other.

关 键 词：连续广义框架 连续广义对偶框架 ε-近似 

分 类 号：O174.2[理学—数学]