Continuous weaving $g$-frames in Hilbert $C^{\ast}$-modules
DOI:
https://doi.org/10.20956/j.v19i3.25230Keywords:
Continuous woven $g$-frames, $g$-frames, Hilbert $C^{*}$-moduleAbstract
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).
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.
