Woven Continuous Generalized Frames in Hilbert C∗-Modules
Main Article Content
Abstract
The aim of this paper is to study woven c-g-frames for Hilbert C∗-modules. We begin by providing some definitions and key properties that are essential for studying this concept. Additionally, we present several properties of woven c-g-frames. Finally, we explore the perturbation theory related to woven c-g-frames.
Article Details
References
- L. Arambaši´c, On Frames for Countably Generated Hilbert C∗-Modules, Proc. Amer. Math. Soc. 135 (2007), 469–478. https://www.jstor.org/stable/20534595.
- N. Assila, H. Labrigui, A. Touri, M. Rossafi, Integral Operator Frames on Hilbert C∗-Modules, Ann. Univ. Ferrara 70 (2024), 1271–1284. https://doi.org/10.1007/s11565-024-00501-z.
- T. Bemrose, P.G. Casazza, K. Gröchenig, M.C. Lammers, R.G. Lynch, Weaving Frames, Oper. Matrices (2016), 1093–1116. https://doi.org/10.7153/oam-10-61.
- P.G. Casazza, D. Freeman, R.G. Lynch, Weaving Schauder Frames, J. Approx. Theory 211 (2016), 42–60. https://doi.org/10.1016/j.jat.2016.07.001.
- P.G. Casazza, R.G. Lynch, Weaving Properties of Hilbert Space Frames, in: 2015 International Conference on Sampling Theory and Applications, IEEE, Washington, DC, USA, 2015: pp. 110–114. https://doi.org/10.1109/SAMPTA.2015.7148861.
- I. Daubechies, A. Grossmann, Y. Meyer, Painless Nonorthogonal Expansions, J. Math. Phys. 27 (1986), 1271–1283. https://doi.org/10.1063/1.527388.
- R.J. Duffin, A.C. Schaeffer, A Class of Nonharmonic Fourier Series, Trans. Amer. Math. Soc. 72 (1952), 341–366. https://doi.org/10.1090/S0002-9947-1952-0047179-6.
- R. El Jazzar, R. Mohamed, On Frames in Hilbert Modules Over Locally C∗-Algebras, Int. J. Anal. Appl. 21 (2023), 130. https://doi.org/10.28924/2291-8639-21-2023-130.
- D. Gabor, Theory of Communication, J. Inst. Electr. Eng. 93 (1946), 445–457. https://doi.org/10.1049/ji-3-2.1946.0076.
- M. Ghiati, M. Rossafi, M. Mouniane, H. Labrigui, A. Touri, Controlled Continuous ∗-g-Frames in Hilbert C∗- Modules, J. Pseudo-Differ. Oper. Appl. 15 (2024), 2. https://doi.org/10.1007/s11868-023-00571-1.
- A. Karara, M. Rossafi, A. Touri, K-Biframes in Hilbert Spaces, J. Anal. 33 (2025), 235–251. https://doi.org/10.1007/s41478-024-00831-3.
- I. Kaplansky, Modules Over Operator Algebras, Amer. J. Math. 75 (1953), 839–858. https://doi.org/10.2307/2372552.
- M.R. Kouchi, A. Nazari, Continuous g-Frame in Hilbert C∗-Modules, Abstr. Appl. Anal. 2011 (2011), 361595. https://doi.org/10.1155/2011/361595.
- A. Lfounoune, R. El Jazzar, K-Frames in Super Hilbert C∗-Modules, Int. J. Anal. Appl. 23 (2025), 19. https://doi.org/10.28924/2291-8639-23-2025-19.
- V.M. Manuilov, E.V. Troitsky, Hilbert C∗-Modules, Translations of Mathematical Monographs, Vol. 226, American Mathematical Society, Providence, Rhode Island, 2005.
- H. Massit, M. Rossafi, C. Park, Some Relations between Continuous Generalized Frames, Afr. Mat. 35 (2024), 12. https://doi.org/10.1007/s13370-023-01157-2.
- F. Nhari, R. Echarghaoui, M. Rossafi, K-g-Fusion Frames in Hilbert C∗-Modules, Int. J. Anal. Appl. 19 (2021), 836–857. https://doi.org/10.28924/2291-8639-19-2021-836.
- W.L. Paschke, Inner Product Modules Over B∗-Algebras, Trans. Amer. Math. Soc. 182 (1973), 443–468. https://doi.org/10.2307/1996542.
- M. Rossafi, F. Nhari, Controlled K-g-Fusion Frames in Hilbert C∗-Modules, Int. J. Anal. Appl. 20 (2022), 1. https://doi.org/10.28924/2291-8639-20-2022-1.
- M. Rossafi, F. Nhari, K-g-Duals in Hilbert C∗-Modules, Int. J. Anal. Appl. 20 (2022), 24. https://doi.org/10.28924/2291-8639-20-2022-24.
- M. Rossafi, F.D. Nhari, C. Park, S. Kabbaj, Continuous G-Frames with C∗-Valued Bounds and Their Properties, Complex Anal. Oper. Theory 16 (2022), 44. https://doi.org/10.1007/s11785-022-01229-4.
- M. Rossafi, S. Kabbaj, Generalized Frames for B(H,K), Iran. J. Math. Sci. Inform. 17 (2022), 1–9. https://doi.org/10.52547/ijmsi.17.1.1.
- M. Rossafi, M. Ghiati, M. Mouniane, F. Chouchene, A. Touri, S. Kabbaj, Continuous Frame in Hilbert C∗-Modules, J. Anal. 31 (2023), 2531–2561. https://doi.org/10.1007/s41478-023-00581-8.
- M. Rossafi, F. Nhari, A. Touri, Continuous Generalized Atomic Subspaces for Operators in Hilbert Spaces, J. Anal. (2024). https://doi.org/10.1007/s41478-024-00869-3.
- M. Rossafi, S. Kabbaj, ∗-K-operator Frame for End∗A(H), Asian-Eur. J. Math. 13 (2020), 2050060. https://doi.org/10.1142/S1793557120500606.
- M. Rossafi, S. Kabbaj, Operator Frame for End∗A(H), J. Linear Topol. Algebra 8 (2019), 85-95.
- M. Rossafi, S. Kabbaj, ∗-K-g-frames in Hilbert A-modules, J. Linear Topol. Algebra 7 (2018), 63-71.
- M. Rossafi, S. Kabbaj, ∗-g-frames in tensor products of Hilbert C∗-modules, Ann. Univ. Paedagog. Crac. Stud. Math. 17 (2018), 17-25.