Perturbation of frames and Riesz bases in Hilbert C*-modules

被引：20

作者：

Han, Deguang ^{[2
]}

Jing, Wu ^{[1
]}

Mohapatra, Ram N. ^{[2
]}

机构：

[1] Fayetteville State Univ, Dept Math & Comp Sci, Fayetteville, NC 28301 USA

[2] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 431卷 / 5-7期

关键词：

Perturbations; Frames; Riesz bases; Hilbert C*-modules;

D O I：

10.1016/j.laa.2009.03.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We extend the Casazza-Christensen general perturbation theorem for Hilbert space frames to modular frames in Hilbert C*-modules. In the Hilbert space setting, under the same perturbation condition, the perturbation of any Riesz basis remains to be a Riesz basis. However, this result is no longer true for Riesz bases in Hilbert C*-modules. We obtain a necessary and sufficient condition under which the perturbation (under Casazza-Christensen's perturbation condition) of Riesz bases of Hilbert C*-modules remains to be Riesz bases. Published by Elsevier Inc.

引用

页码：746 / 759

页数：14

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