Some new properties of g-frame in Hilbert C*-modules

Mohamed Rossafi; Hatim Labrigui

doi:10.20956/j.v18i3.20288

Authors

Mohamed Rossafi Faculty of Sciences, Dhar El Mahraz University Sidi Mohamed Ben Abdellah, Fes,
Hatim Labrigui

DOI:

https://doi.org/10.20956/j.v18i3.20288

Keywords:

Frame, modular Riesz basis, modular $g$-Riesz basis, $C^{\ast}$-algebra, Hilbert $\mathcal{A}$-modules

Abstract

The theory of frames which appeared in the last half of the century, has been generalized rapidly and various generalizations of frames in Hilbert spaces and Hilbert $C^{\ast}$-modules. In this paper, we will give some new properties of modular Riesz basis and modular $g$-Riesz basis that present a generalization of the results established in a Hilbert space.

References

bibitem{alijani} A. Alijani and M. A. Dehghan, emph{$ast$-frames in Hilbert $C^{ast}$-modules}, U.P.B. Sci. Bull, Ser. A, vol. 73, no. 4, pp. 89-106, 2011.

bibitem{Ara} L. Arambav{s}i'{c}, emph{On frames for countably generated Hilbert $mathcal{C}^{ast}$-modules}, Proc. Amer. Math. Soc., vol. 135, pp. 469-478, 2007.

bibitem{13} I. Daubechies, A. Grossmann, and Y. Meyer, emph{Painless nonorthogonal expansions}, J. Math. Phys., vol. 27, pp. 1271-1283, 1986.

bibitem{Duf} R. J. Duffin and A. C. Schaeffer, "A class of nonharmonic fourier series", emph{Trans. Amer. Math. Soc.}, vol. 72, pp. 341-366, 1952.

bibitem{F4} M. Frank, D. R. Larson, emph{Frames in Hilbert $mathcal{C}^{ast}$-modules and $mathcal{C}^{ast}$-algebras}", J. Oper. Theory, vol. 48, pp. 273-314, 2002.

bibitem{Gab} D. Gabor, emph{Theory of communications}, J. Elec. Eng., vol. 93, pp. 429-457, 1946.

bibitem{Pas} W. Paschke, emph{Inner product modules over $B^{ast}$-algebras}, Trans. Amer. Math. Soc., vol. 182, pp. 443-468, 1973.

bibitem{AB} A. Khorsavi, B. Khorsavi, emph{Fusion frames and g-frames in Hilbert $mathcal{C}^{ast}$-modules}, Int. J.Wavelet, Multiresolution

and Information Processing 6 (2008), pp. 433-446.

bibitem{GFR} Zhong-Qi Xiang and Yong-Ming Li, emph{$G$-frames for operators in Hilbert $C^{ast}$-modules}, Turkish Journal of Mathematics, vol 40, pp. 453-469, 2016.

bibitem{AAA} A. Khosravi and M. R. Farmani, Frames and $g$-frame in Hilbert Spaces, Mathematics and computational sciences, Vol 3(1), pp.10-16, 2022.

bibitem{BBB} A. Khosravi and B. Khosravi, $g$-frames and modular Riesz basis in Hilbert $C^{ast}$-modules, International Journal of Wavelets, Multirsolution and Information Processing, Vol 10, No. 2, 12 pages, 2012.

bibitem{DHW} Deguan Han, Wu Jing, David Larson, Ram N. Mohapatra, Riesz Bases and their dual mudular frames in Hilbert $C^{ast}$-modules, Mathematical Analysis and Applications, Vol 343 , pp. 246-256, 2008.