Woven generalized fusion frame in Hilbert $C^{\ast}-$module
DOI:
https://doi.org/10.20956/j.v19i1.21791Keywords:
Fusion frame, g-fusion frame, woven g-fusion frame, $C^{\ast}$-algebras, Hilbert $C^{\ast}$-modulesAbstract
The notion of weaving was recently proposed to simulate a question in distributed signal processing and wireless sensor networks.
In this paper we introduced the notion of a woven $g-$fusion frame in Hilbert $C^{\ast}-$modules, also we gives some properties. Finallly we study perturbation of weaving $g-$fusion frames.
References
Alijani A, 2015. Generalized frames with C∗-valued bounds and their operator duals, Filomat 29:7,
–1479. DOI 10.2298/FIL1507469A
Alijani A, Dehghan M, 2011. ∗-Frames in Hilbert C∗-modules, Politehn. Univ. Bucharest Sci. Bull.Ser. A Appl. Math. Phys. 73, no. 4, 89–106.
Arambaˇsi´c L, 2007. On frames for countably generated Hilbert C∗-modules, Proc. Am. Math. Soc.135, 469–478.
Bemrose T, Casazza P. G, Grochenig K, Lammers M. C, Lynch R. G, 2016. Weaving frames, Oper.Matrices, 10, 1093–1116.
Bounader N, Kabbaj S, 2014. ∗-g-frames in Hilbert C∗-modules, J. Math. Comput. Sci. 4, No. 2,246-256.
Duffin R. J, Schaeffer A. C, 1952. A class of nonharmonic fourier series, Trans. Am. Math. Soc.72, 341–366.
Fang X, Moslehian M. S, Xu Q, 2018. On majorization and range inclusionof operators on Hilbert C∗-modules, Linear Multilinear Algebra. 66, 2493 2500. https://doi.org/10.1080/03081087.2017.1402859.
Frank M, Larson D. R, 2000. A-module frame concept for Hilbert C∗-modules, functinal and harmonicanalysis of wavelets, Contempt. Math. 247, 207-233.
Gabor D, 1946. Theory of communications, J. Elect. Eng. 93 (1946), 429–457.
Ghobadzadeh F, Najati A, Anastassiou G. A, Park C, 2018. Woven frames in Hilbert C∗−modules,J. Comput. Anal. Appl. 25, 1220–1232.
Kabbaj S, Rossafi M, 2018. ∗-Operator frame for End∗ A(H), Wavelet Linear Algebra, 5, 1-13.https://doi.org/10.22072/WALA.2018.79871.1153
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.
Lance E. C, 1995. Hilbert C∗−Modules: A Toolkit for Operator Algebraist, London Math. Soc.Lecture Note Ser. Cambridge Univ. Press, Cambridge.
Nhari F. D, Echarghaoui R, Rossafi M, 2021. K −g−fusion frames in Hilbert C∗−modules, Int. J.Anal. Appl. 19 (6).
Paley R, Wiener N, 1987. Fourier Transforms in Complex Domains, Am. Math. Soc. Colloq. Publ.19, Am. Math. Soc., Providence, RI.
Rossafi M, Nhari FD, Park C, Kabbaj S, 2022. Continuous g-Frames with C∗-Valued Bounds andTheir Properties. Complex Anal. Oper. Theory 16, 44. https://doi.org/10.1007/s11785-022-01229-4
Rossafi M, Kabbaj S, 2020. ∗-K-operator frame for End∗ A(H), Asian-Eur. J. Math. 13, 2050060.https://doi.org/10.1142/S1793557120500606.
Rossafi M, Kabbaj S, 2019. Operator frame for End∗ A(H), J. Linear Topol. Algebra, 8, 85-95.
Rossafi M, Kabbaj S, 2018. ∗-K-g-frames in Hilbert A-modules, J. Linear Topol. Algebra, 7, 63-71.
Rossafi M, Kabbaj S, 2018. ∗-g-frames in tensor products of Hilbert C∗-modules, Ann. Univ.Paedagog. Crac. Stud. Math. 17, 17-25.
Zhao X, Li P, 2021. Weaving Frames in Hilbert C∗-Modules, Journal of Mathematics, vol. 2021,Article ID 2228397, 13 pages.
Xiang Z, LI Y, 2016. G−frames for operators in Hilbert C∗−modules, Turk J Math, 40, 453-469.Doi: 10.3906/mat-1501-22
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 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.