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.
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