Woven generalized fusion frame in Hilbert $C^{\ast}-$module


  • Fakhr-dine Nhari Dhar El Mahraz University, Morocco
  • Mohamed Rossafi Dhar El Mahraz University, Morocco




Fusion frame, g-fusion frame, woven g-fusion frame, $C^{\ast}$-algebras, Hilbert $C^{\ast}$-modules


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.


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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






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