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
  • [21] On Weaving g-Frames for Hilbert Spaces
    Dongwei Li
    Jinsong Leng
    Tingzhu Huang
    Xiaoping Li
    Complex Analysis and Operator Theory, 2020, 14
  • [22] On Weaving g-Frames for Hilbert Spaces
    Li, Dongwei
    Leng, Jinsong
    Huang, Tingzhu
    Li, Xiaoping
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2020, 14 (02)
  • [23] APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES
    Khosravi, Amir
    Azandaryani, Morteza Mirzaee
    ACTA MATHEMATICA SCIENTIA, 2014, 34 (03) : 639 - 652
  • [24] Operator representations of g-frames in Hilbert spaces
    Li, Dongwei
    Leng, Jinsong
    LINEAR & MULTILINEAR ALGEBRA, 2020, 68 (09) : 1861 - 1877
  • [25] G-FRAMES AND HILBERT-SCHMIDT OPERATORS
    Abdollahpour, M. R.
    Najati, A.
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2011, 37 (04): : 141 - 155
  • [26] Moment Problem of G-frames in Hilbert Spaces
    Wang, Xiangyang
    Shu, Zhibiao
    2011 TENTH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING AND APPLICATIONS TO BUSINESS, ENGINEERING AND SCIENCE (DCABES), 2011, : 51 - 55
  • [27] Characterizations and redundancies of g-frames in Hilbert spaces
    Xiao, Xiangchun
    Zhao, Guoping
    Zhou, Guorong
    LINEAR & MULTILINEAR ALGEBRA, 2024, 72 (04) : 547 - 562
  • [28] On sum and stability of g-frames in Hilbert spaces
    Li, Dongwei
    Leng, Jinsong
    Huang, Tingzhu
    Sun, Guomin
    LINEAR & MULTILINEAR ALGEBRA, 2018, 66 (08) : 1578 - 1592
  • [29] Controlled G-Frames and Their G-Multipliers in Hilbert spaces
    Rahimi, Asghar
    Fereydooni, Abolhassan
    ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2013, 21 (02): : 223 - 236
  • [30] G-frames as Sums of Some g-orthonormal Bases
    Abdollahpour, Mohammad Reza
    Najati, Abbas
    KYUNGPOOK MATHEMATICAL JOURNAL, 2013, 53 (01): : 135 - 141
12345