连续广义框架的ε-近似

ε-approximations of continuous generalized frames

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.