K-g-Fusion Frames in Hilbert C∗-Modules

Main Article Content

Fakhr-dine Nhari, Rachid Echarghaoui, Mohamed Rossafi


In this paper, we introduce the concepts of g-fusion frame and K-g-fusion frame in Hilbert C∗-modules and we give some properties. Also, we study the stability problem of g-fusion frame. The presented results extend, generalize and improve many existing results in the literature.

Article Details


  1. R. J. Duffin, A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341-366.
  2. D. Gabor, Theory of communications, J. Elec. Eng. 93 (1946), 429-457.
  3. A. Khorsavi, B. Khorsavi, Fusion frames and g-frames in Hilbert C ∗-modules, Int. J. Wavelet Multiresolution Inform. Process. 6 (2008), 433-446.
  4. A. Alijani, M. Dehghan, ∗-frames in Hilbert C ∗modules, U. P. B. Sci. Bull. Ser. A. 2011.
  5. M. Frank, D. R. Larson, A-module frame concept for Hilbert C ∗-modules, Funct. Harmonic Anal. Wavelets Contempt. Math. 247 (2000), 207-233.
  6. I. Kaplansky, Modules over operator algebras, Amer. J. Math. 75 (1953), 839-858.
  7. Lj. Arambaˇsi´c, On frames for countably generated Hilbert C∗-modules, Proc. Amer. Math. Soc. 135 (2007), 469-478.
  8. W. Paschke, Inner product modules over B∗-algebras, Trans. Amer. Math. Soc. (182) (1973), 443-468.
  9. M. Rossafi, S. Kabbaj, ∗-g-frames in tensor products of Hilbert C∗-modules, Ann. Univ. Paedagog. Crac. Stud. Math. 17 (2018), 17-25.
  10. M. Rossafi, S. Kabbaj, ∗-K-g-frames in Hilbert A-modules, J. Linear Topol. Algebra, 7 (2018), 63-71.
  11. M. Rossafi, S. Kabbaj, Operator Frame for End∗ A(H), J. Linear Topol. Algebra, 8 (2019), 85-95.
  12. S. Kabbaj, M. Rossafi, ∗-operator Frame for End∗ A(H), Wavelet Linear Algebra, 5 (2) (2018), 1-13.
  13. M. Rossafi, S. Kabbaj, ∗-K-operator frame for End∗ A(H), Asian-Eur. J. Math. 13(3) (2020), 2050060.
  14. X. Fang, J. Yu, H. Yao, Solutions to operator equations on Hilbert C∗−modules, Linear Algebra Appl. 431 (2009), 2142- 2153.