p-框架、Hilbert-Schauder框架与σ-框架算子  

p-frames, Hilbert-Schauder frames and σ-frame operators

作　　者：林丽琼[1] 张云南[2] 朱玉灿[1] LIN Li Qiong ZHANG YunNan ZHU YuCan

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：《中国科学：数学》2016年第12期1791-1800,共10页Scientia Sinica：Mathematica

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

摘　　要：鉴于Banach空间上的框架没有合适的框架算子定义,本文考虑Banach空间上满足一定条件的一类序列,把它称为σ-框架,并相应于这类序列给出σ-框架算子的概念.σ-框架及其σ-框架算子是Hilbert空间上框架及其框架算子的自然推广.本文说明σ-框架算子是正的、自共轭的、可通过l_2分解的,并得到σ-框架在算子摄动下的结果.本文还说明σ-框架包含Banach空间上的另外两类框架—p-框架(1<p≤2)和σHS(σHilbert-Schauder)框架,其中σHS是根据HS(Hilbert-Schauder)框架的定义而引入的一类框架,最后还得到了p-框架(1<p≤2)和σHS框架在算子摄动下的结果.In view of the fact that there are not appropriate frame operators of frames in Banach spaces, this paper considers a class of sequences satisfying certain conditions in Banach spaces which is called as the σ-frame, and the corresponding concept of frame operators is given. The σ-frames and σ-frame operators are natural generalizations of frames and frame operators in Hilbert spaces. This paper illustrates that σ-frame operators are positive, self-adjoint and they can be decomposed through 12. The perturbation result under operators of σ-frame is obtained. This paper also shows that the kind of σ-frames contains two other kinds of frames in Banach space-p-frames （1 〈 p ≤ 2） and artS frames which are a kind of frames according to the definition of the Hilbert-Schauder frames. The perturbation results under operators of p-frames （1 〈 p ≤ 2） and artS frames are obtained.

关 键 词：BANACH空间 σ-框架算子 p-框架 Hilbert—Schauder框架 

分 类 号：O177.2[理学—数学]