无穷维Hilbert空间上框架的算子与范数  

Operators and Norms of Frames on Infinite-Dimensional Hilbert Spaces

作　　者：林丽琼[1] 张云南[2] 朱玉灿[1] 

机构地区：[1]福州大学数学与计算机科学学院,福州350108 [2]福建师范大学数学与计算机科学学院,福州350007

出　　处：《数学学报（中文版）》2017年第6期911-918,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11401101,11201071,11171066);福建省自然科学基金资助项目(2013J05004);福州大学基金资助项目(2013-XQ-33)

摘　　要：在框架理论研究中,哪类可逆算子能使得某些框架性质保持不变这个问题是基本和重要的,本文在无穷维Hilbert空间上对下述两个问题进行研究.问题1:哪类可逆算子能使得框架算子保持不变;问题2:哪类可逆算子能使得框架范数只相差一列常数.本文从抽象的算子理论和具体的构造方法两方面对问题1给出解答.利用框架的相容算子的概念,当把问题2中的可逆算子集换成一类较小的算子集时,得到了问题2的回答.In the research of frame theory, the questions that what kinds of invertible operators can make some frame properties remain unchanged are essential and im- portant. This paper study the following two questions on infinite dimensional Hilbert spaces. Question one： what kind of invertible operators can make the frame operators remain unchanged; Question two： what kind of invertible operators can makes the norms of frames are a multiple by a fixed sequence of the norms of original frames. This paper gives the answer of Question one by the abstract operator theory and by the concrete constructions. When limited the class of invertible operators to a smaller class of operators, this paper obtain the answer of Question two by using the concept of admissible operators of frames.

关 键 词：HILBERT空间 框架 框架算子 范数 

分 类 号：O177.1[理学—数学]