JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (6): 49-56.doi: 10.6040/j.issn.1671-9352.0.2015.397

Previous Articles     Next Articles

New perturbation results and characterization on approximately dual g-frames in hilbert spaces

ZHANG Wei1, FU Yan-ling2   

  1. 1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China;
    2. Department of Information Engineering, Henan Finance and Taxation College, Zhengzhou 451464, Henan, China
  • Received:2015-08-24 Online:2016-06-20 Published:2016-06-15

PDF (PC)

647

Abstract: In this paper, some new results on approximately dual g-frames perturbation are presented. An explicit expression and some sufficient conditions for approximately dual g-frames are given.

Key words: perturbation, g-frames, approximately dual g-frames

CLC Number: 

  • O174.2
[1] DUFFIN D J, SCHAEFFER A C. A class of nonharmonic fourier series[J]. Transactions of the American Mathematical Society,1952, 72:341-366.
[2] YOUNG R M. An introduction to nonharmonic fourier series[M]. New York: Academic Press, 1990.
[3] DAUBECHIES I, GROSSMANN A, MEYER Y. Painless nonorthogonal expansions[J]. Journal of Mathematical Physics, 1986, 27:1271-1283.
[4] SUN Wenchang. G-frame and g-Riesz bases[J]. Journal of Mathematical Analysis and Applications, 2006, 322(1):437-452.
[5] CHRISTENSEN O, LAUGESEN R S. Approximately dual frames in Hilbert spaces and application to Gabor frames[J]. Sampling Theory in Signal and Image Processing, 2010, 9(3):77-93.
[6] DING Mingling, ZHU Yucan. G-Besselian frames in Hilbert spaces[J]. Acta Mathematica Sinica(English Series), 2010, 26(11):2117-2130.
[7] KHOSRAVI A, MUSAZADEH K. Fusion frames and g-frames[J]. Journal of Mathematical Analysis and Applications, 2008, 342:1068-1083.
[8] RYNNE B P, YOUNGSON M A. Linear functional analysis[M]. Springer Undergraduate Mathematics Series, 2006.
[9] KHOSRAVI A. Approximate duality of g-frames in Hilbert spaces[J]. Acta Mathematica Scientia, 2014, 34B(3):639-652.
[10] ZHU Yucan. Characterizations of g-Riesz bases in Hilbert spaces[J]. Acta Mathematica Scientia, 2008, 24(10):1727-1736.
[11] 李艳婷,李登峰.广义框架的近似对偶框架的构造及扰动[J]. 河南大学学报(自然科学版), 2015, 45(2):127-130. LI Yanting, LI Dengfeng. The construction and perturbation of approximatrly dual frame for g-frames[J]. Journal of Henan University(Natural Science), 2015, 45(2):127-123.
[1] SONG Liang, FENG Jin-shun, CHENG Zheng-xing. Existence and stability for multiple gabor frames [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 17-24.
[2] SONG Jia-jia, CAO Xiao-hong, DAI Lei. The judgement for the small compact perturbation of SVEP for upper triangular operator matrices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 61-67.
[3] DAI Lei, CAO Xiao-hong. Property(z)and Weyl type theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 60-65.
[4] KONG Ying-ying, CAO Xiao-hong, DAI Lei. Judgement of a-Weyls theorem and its perturbations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 77-83.
[5] DONG Jiong, CAO Xiao-hong. Weyls theorem for the cube of operator and compact perturbations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 15-21.
[6] REN Xue-fang, ZHANG Ling. Perturbation theorems of inverse P-sets and perturbation-based data mining [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 54-60.
[7] WU Xue-li, CAO Xiao-hong, ZHANG Min. The perturbation of the single valued extension property for bounded linear operators [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 5-9.
[8] CHEN Wen, YAO Jing-sun, YANG Xue-jie. A nonlinear mixed boundary value problem for singularly perturbed forth-order differential equation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(03): 67-72.
[9] CUI Miao-miao, WANG Bi-yu, CAO Xiao-hong. A note on operator matrixs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 56-61.
[10] YANG Xue-jie, SUN Guo-zheng*, CHEN Wen. Shock solution for a quasilinear singularly perturbed problem#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 79-83.
[11] WANG Bi-yu, CAO Xiao-hong*. The perturbation for the Browder’s theorem of operator matrix#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 90-95.
[12] YU Wei, CAO Xiao-hong*. Topological uniform descent and the single valued extension property [J]. J4, 2013, 48(4): 10-14.
[13] ZHAO Hai-yan, CAO Xiao-hong*. The stability of the property (ω1) for the Helton class operators [J]. J4, 2013, 48(4): 15-19.
[14] WANG Gai-ling, CAO Xiao-hong*. Judgement for the property (ω′) and the generalized property (ω′) [J]. J4, 2012, 47(4): 11-16.
[15] LIU Ai-fang, LI Na-na, CAO Xiao-hong*. Generalized Kato type and generalized property (ω′) [J]. J4, 2012, 47(4): 17-23.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd