G-Frames and g-Frame Sequences in Hilbert Spaces

作     者：Yan Jin WANG Yu Can ZHU~(1))Department of Mathematics,Fuzhou University,Fuzhou 350002,P. R. China 

作者机构：Department of Mathematics Fuzhou University Fuzhou 350002 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2009年第25卷第12期

页      面：2093-2106页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Natural Science Foundation of Fujian Province of China (No.2009J01007) Education Commission Foundation of Fujian Province of China (No.JA08013) 

主　　题：frame g-Bessel sequence g-frame g-frame sequence 

摘      要：In this paper, we first determine the relations among the best bounds A and B of the g-frame, the g-frame operator S and the pre-frame operator Q and give a necessary and sufficient condition for a g-frame with bounds A and B in a complex Hilbert space. We also introduce the definition of a g-frame sequence and obtain a necessary and sufficient condition for a g-frame sequence with bounds A and B in a complex Hilbert space. Lastly, we consider the stability of a g-frame sequence for a complex Hilbert space under perturbation.