Perturbations of Invertible Operators and Stability of g-Frames in Hilbert Spaces

被引：9

作者：

Guo, Xunxiang ^{[1
]}

机构：

[1] Southwestern Univ Finance & Econ, Dept Math, Chengdu 611130, Peoples R China

来源：

RESULTS IN MATHEMATICS | 2013年 / 64卷 / 3-4期

关键词：

G-frame; G-Riesz basis; perturbation; invertible operator; stability; G-RIESZ BASES;

D O I：

10.1007/s00025-013-0323-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the perturbations of invertible operators and stability of g-frames in Hilbert spaces. In particular, we obtain some conditions under which the perturbations of an invertible operator are still an invertible operator, the perturbations of a right invertible operator or a surjective operator are still a right invertible operator or surjective operator. Then we apply the perturbations of invertible operators to study the stability of g-frames which is close related with the invertibility (or right invertibility) property of operators.

引用

页码：405 / 421

页数：17

共 20 条

[1]

[Anonymous], 2000, MEM AM MATH SOC

[2]

[Anonymous], 2016, Appl. Numer. Harmon. Anal

[3]

[Anonymous], J FOURIER ANAL APPL

[4] A PALEY-WIENER THEOREM FOR FRAMES [J].

CHRISTENSEN, O .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (07) :2199-2201

[5]

Chui C.K., 2014, An introduction to wavelets, DOI DOI 10.1109/99.388960

[6]

Daubechies I., 1992, CBMS NSF REGIONAL C, V61

[7] g-Besselian frames in Hilbert spaces [J].

Ding, Ming Ling ;

Zhu, Yu Can .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2010, 26 (11) :2117-2130

[8] A CLASS OF NONHARMONIC FOURIER SERIES [J].

DUFFIN, RJ ;

SCHAEFFER, AC .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1952, 72 (MAR) :341-366

[9] ON THE STABILITY OF FRAMES AND RIESZ BASES [J].

FAVIER, SJ ;

ZALIK, RA .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1995, 2 (02) :160-173

[10] g-Bases in Hilbert Spaces [J].

Guo, Xunxiang .

ABSTRACT AND APPLIED ANALYSIS, 2012,

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