Characterizations of g-Frames and g-Riesz Bases in Hilbert Spaces  

作　　者：Yu Can ZHU 

机构地区：[1]Department of Mathematics, Fuzhou University, Fuzhou 350002 [2] P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第10期1727-1736,共10页数学学报（英文版）

基　　金：the Natural Science Foundation of Fujian Province,China (No.Z0511013);the Education Commission Foundation of Fujian Province,China (No.JB04038)

摘　　要：In this paper, we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space, which will play a key role in studying g-frames and g-Riesz bases etc. Using the pre-frame operator Q, we give some necessary and sufficient conditions for a g-Bessel sequence, a g-frame, and a g-Riesz basis in a complex Hilbert space, which have properties similar to those of the Bessel sequence, frame, and Riesz basis respectively. We also obtain the relation between a g-frame and a g-Riesz basis, and the relation of bounds between a g-frame and a g-Riesz basis. Lastly, we consider the stability of a g-frame or a g-Riesz basis for a Hilbert space under perturbation.In this paper, we introduce the pre-frame operator Q for the g-frame in a complex Hilbert space, which will play a key role in studying g-frames and g-Riesz bases etc. Using the pre-frame operator Q, we give some necessary and sufficient conditions for a g-Bessel sequence, a g-frame, and a g-Riesz basis in a complex Hilbert space, which have properties similar to those of the Bessel sequence, frame, and Riesz basis respectively. We also obtain the relation between a g-frame and a g-Riesz basis, and the relation of bounds between a g-frame and a g-Riesz basis. Lastly, we consider the stability of a g-frame or a g-Riesz basis for a Hilbert space under perturbation.

关 键 词：FRAME g-Bessel sequence G-FRAME g-Riesz basis 

分 类 号：O14[理学—数学]