Controlled g-frames and their dual in Hilbert $C^{\ast}-$modules
DOI:
https://doi.org/10.20956/j.v20i1.26361Keywords:
g-frame, controlled g-frame, $C^{\ast}$-algebras, Hilbert $C^{\ast}$-modulesAbstract
In this paper we give some new results for controlled g-frames and controlled dual g-frames in Hilbert $C^*$-modules.
First, we talk about controlled g-frame characterisation and find certain conditions that are equal to them.
Then, we explain the purpose controlled dual g-frames and controlled dual g-frames operator and discuss some of their characteristics.
References
Balazs P, Antoine J. P, Grybos A, 2010. Weighted and controlled frames, Int. J. Wavelets Multiresolut. Inf.
Process., 8(1) 109-132.
Christensen O, 2016. An Introduction to Frames and Riesz bases, Birkhauser.
Conway J. B, 2000. A Course In Operator Theory, Am. Math. Soc., Providence, RI.
Daubechies I, Grossmann A, Meyer Y, 1986. Painless nonorthogonal expansions, J. Math. Phys. 27, 1271{
Dun R. J, Schae er A. C, 1952. A class of nonharmonic fourier series, Trans. Am. Math. Soc. 72, 341{366.
Hua D, Huang Y, 2017. Controlled K - g-frames in Hilbert spaces, Results in Math., 72(3), 1227-1238.
Jing W, 2006. Frames in Hilbert C*-modules, Doctoral Dissertation.
Kabbaj S, Rossa M, 2018. -operator Frame for End
A(H), Wavelet Linear Algebra, 5, (2), 1-13.
Kaplansky I, 1953. Modules over operator algebras, Am. J. Math. 75, 839{858.
Khorsavi A, Khorsavi B, 2008. Fusion frames and g-frames in Hilbert C-modules, Int. J. Wavelet, Multiresolution
and Information Processing 6, 433-446. Doi: doi.org/10.1142/S0219691308002458
Kouchi M. R, Rahimi A, 2017. On controlled frames in Hilbert C*-modules, Int. J. Walvelets Multi. Inf.
Process., 15(4), 1750038.
Lance E. C, 1995. Hilbert C*-Modules: A Toolkit for Operator Algebraists, London Math. Soc. Lecture
Note Ser., vol. 210, Cambridge Univ. Press.
Rossa M, Kabbaj S, 2020. -K-operator Frame for End
A(H), Asian-Eur. J. Math. 13, 2050060.
Xiao X. C, Zeng X. M, 2010. Some properties of g-frames in Hilbert C*-modules, J. Math. Anal. Appl., 363,
-408.
Sahu N. K, 2021. Controlled g-frames in Hilbert C*-modules, Mathematical Analysis and its Contemporary
Applications Volume 3, Issue 3, 65{82.
Sun W, 2006. G-frames and g-Riesz bases, J. Math. Anal. Appl. 322, no 1, 437-452.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Author and publisher
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license. This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.