g-FRAMES AND MODULAR RIESZ BASES IN HILBERT C*-MODULES

被引：21
作者：
Khosravi, Amir [1 ]
Khosravi, Behrooz [2 ]
机构：
[1] Tarbiat Moallem Univ, Fac Math Sci & Comp, Tehran 15618, Iran
[2] Amir Kabir Univ Technol, Fac Math & Comp Sci, Dept Pure Math, Tehran Polytech, Tehran 15914, Iran
来源：
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING | 2012年 / 10卷 / 02期
关键词：
g-frame; g-Riesz basis; modular g-Riesz basis; Hilbert C*-module; modular Riesz basis; FUSION FRAMES; SPACES;
D O I：
10.1142/S0219691312500130
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
In this paper we introduce modular Riesz basis, modular g-Riesz basis in Hilbert C*-modules in a very natural way and we show that they share many properties with Riesz basis and g-Riesz basis in Hilbert spaces. We also found that by using the fact that every finitely or countably generated Hilbert C*-module over a unital C*-algebra has a standard Parseval frame, we characterize g-frames, modular Riesz bases and modular g-Riesz bases. Finally we obtain a perturbation result for modular g-Riesz bases.
引用
收藏
页数：12
相关论文
共 50 条
  • [31] FRAMES IN HILBERT C*-MODULES
    Alijani, A.
    Dehghan, M. A.
    UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2011, 73 (04): : 89 - 106
  • [32] FUSION FRAMES AND G-FRAMES IN TENSOR PRODUCT AND DIRECT SUM OF HILBERT SPACES
    Khosravi, Amir
    Azandaryani, M. Mirzaee
    APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2012, 6 (02) : 287 - 303
  • [33] ON REDUNDANCY, DILATIONS AND CANONICAL DUALS OF g-FRAMES IN HILBERT SPACES
    Guo, Xunxiang
    BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2015, 9 (04) : 81 - 99
  • [34] Characterization and stability of approximately dual g-frames in Hilbert spaces
    Fu, Yan-Ling
    Zhang, Wei
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018,
  • [35] Perturbations of Invertible Operators and Stability of g-Frames in Hilbert Spaces
    Guo, Xunxiang
    RESULTS IN MATHEMATICS, 2013, 64 (3-4) : 405 - 421
  • [36] Fusion frames and g-frames
    Khosravi, Amir
    Musandeh, Kamran
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 342 (02) : 1068 - 1083
  • [37] Excess of a class of g-frames
    Zang, Lili
    Sun, Wenchang
    Chen, Dianfa
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 352 (02) : 711 - 717
  • [38] On∗-fusion frames for Hilbert C∗-modules
    Assila, Nadia
    Kabbaj, Samir
    Zoubeir, Hicham
    ADVANCES IN OPERATOR THEORY, 2024, 9 (02)
  • [39] G-frames as special frames
    Askarizadeh, Abas
    Dehghan, Mohammad Ali
    TURKISH JOURNAL OF MATHEMATICS, 2013, 37 (01) : 60 - 70
  • [40] Some Properties of Controlled K-g-Frames in Hilbert C*-Modules
    Echarghaoui, Rachid
    Ghiati, M'hamed
    Mouniane, Mohammed
    Rossafi, Mohamed
    INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2022, 20
12345