Continuous weaving $g$-frames in Hilbert $C^{\ast}$-modules

M'hamed Ghiati; Mohammed Mouniane; Nadia Assila; Mohamed Rossafi

doi:10.20956/j.v19i3.25230

Authors

M'hamed Ghiati
Mohammed Mouniane
Nadia Assila
Mohamed Rossafi Faculty of Sciences, Dhar El Mahraz University Sidi Mohamed Ben Abdellah, Fes,

DOI:

https://doi.org/10.20956/j.v19i3.25230

Keywords:

Continuous woven $g$-frames, $g$-frames, Hilbert $C^{*}$-module

Abstract

The present paper aims to study $c$-$g$-woven for Hilbert $C^ {*} $-module spaces, first, we give some definitions and fundamental properties which will be useful to introduce the notion. And also some of his properties are given. Finally, we discuss the perturbation for $c$-$g$-woven.

References

bibitem{Aram2006} L. Arambašić, On frames for countably generated Hilbert $C^{*}$-modules, Proc. Am. Math. Soc. 135 (2006) 469–478. url{https://doi.org/10.1090/S0002-9939-06-08498-X.}

bibitem{Bemrose2016}

T. Bemrose, P.G. Casazza, K. Gröchenig, M.C. Lammers, R.G. Lynch, Weaving frames, Oper. Matrices. 10 (2016) 1093–1116. url{https://doi.org/10.7153/oam-10-61.}

bibitem{Casazza1997}

P.G. Cazassa, O. Christensen, Perturbation of Operators and Applications to Frame Theory, J. Fourier Anal. Appl. 3 (1997). url{https://doi.org/10.1007/bf02648883.}

bibitem{Duffin1952} R. J. Duffin, and A. C. Schaeffer, A Class of Nonharmonic Fourier Series, Trans. Amer. Math. Soc. (1952) 341-366.

bibitem{ghiati2022} M. Ghiati, S. Kabbaj, H. Labrigui, A. Touri, M. Rossafi, $*$-$K$-$g$-frames and their duals for Hilbert A-modules, J. Math. Comput. Sci., 12 (2022), Article ID 5

bibitem{GhiatiAsia} M. Ghiati, M. Rossafi and S. Kabbaj, New Properties of Controlled Continuous $K$-$g$-Frames in Hilbert $C^{*}$-Modules. Asian J. Math. Appl. 2022. 12.

bibitem{Kouchi2011} M. R. Kouchi and A. Nazari, Continuous $g$-frames in Hilbert $C^{*}$-modules, Hindawi Publishing Corporation Abstract and Applied Analysis Volume (2011), Article ID 361595, 20 pages.

bibitem{Lance1995}

E. C. Lance, Hilbert $C^{*}$-Modules: A Toolkit for Operator Algebraist, 144 pages, vol. 210 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, (1995).

bibitem{Paschke1973}

W.L. Paschke, Inner product modules over $B*$-algebras, Trans. Am. Math. Soc. 182 (1973) 443–468.

url{https://doi.org/10.1090/s0002-9947-1973-0355613-0.}

bibitem{Rossafi20182}

M. Rossafi, S. Kabbaj, Frames and Operator Frames for B ( H ), Asia Math. 2 (2018) 19–23.

bibitem{Rossafi2018}

M. Rossafi, S. Kabbaj, $*$-$K$-$g$-frames in Hilbert $mathcal{A}$-modules, J. Linear Topol. Algebr. 7 (2018) 63–71.

bibitem{Rossafi2020definition}

M. Rossafi, F. Chouchene, and S. Kabbaj, Integral Frame in Hilbert $C^{ast}$-Modules. url{https://arxiv.org/abs/2005.09995v2}

bibitem{Vashisht2017}

L.K. Vashisht, Deepshikha, On continuous weaving frames, Adv. Pure Appl. Math. 8 (2017) 15–31. url{https://doi.org/10.1515/apam-2015-0077.}

bibitem{Xu2008}

Q. Xu, L. Sheng, Positive semi-definite matrices of adjointable operators on Hilbert $C^{*}$-modules, Linear Algebra Appl. 428 (2008) 992–1000. url{https://doi.org/10.1016/j.laa.2007.08.035.}

bibitem{Yosida1980} K. Yosida, Functional Analysis, vol. 123, Springer-Verlag Berlin Heidelberg, Springer, Berlin, Germany, 6th edition, (1980).