K-g-Duals in Hilbert C∗-Modules

Main Article Content

Mohamed Rossafi
Fakhr-dine Nhari


Generalized frames with adjointable operators called K-g-frame is a generalization of a g-frame. In this paper, we give some results of dual K-g-bessel sequence, finally we obtain a new properties of approximate K-g-duals in Hilbert C∗-module.

Article Details


  1. 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.
  2. D. Gabor, Theory of Communication, J. Inst. Electric. Eng. 93 (1946), 429-457.
  3. A. Khosravi, B. Khosravi, Fusion Frames and g-Frames in Hilbert C*-Modules, Int. J. Wavelets Multiresolut. Inf. Process. 06 (2008), 433–446. https://doi.org/10.1142/S0219691308002458.
  4. M. Frank, D.R. Larson, A Module Frame Concept for Hilbert C*-Modules, in: L.W. Baggett, D.R. Larson (Eds.), Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 1999: pp. 207–233. https://doi.org/10.1090/conm/247/03803.
  5. E.C. Lance, Hilbert C*-modules: A Toolkit for Operator Algebraists, London Mathematical Society Lecture Note Series, 210, Cambridge University Press, Cambridge, 1995.
  6. S. Kabbaj, M. Rossafi, ∗-Operator Frame for End∗A(H), Wavelet Linear Algebra, 5 (2018), 1-13.
  7. I. Kaplansky, Modules Over Operator Algebras, Amer. J. Math. 75 (1953), 839. https://doi.org/10.2307/2372552.
  8. F.D. Nhari, R. Echarghaoui, M. Rossafi, K − g−Fusion Frames in Hilbert C∗-Modules, Int. J. Anal. Appl. 19 (6) (2021), 836-857. https://doi.org/10.28924/2291-8639-19-2021-836.
  9. 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.
  10. M. Rossafi, F.D. 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.
  11. M. Rossafi, S. Kabbaj, ∗-K-Operator Frame for End∗A(H), Asian-Eur. J. Math. 13 (2020), 2050060. https://doi.org/10.1142/S1793557120500606.
  12. M. Rossafi, S. Kabbaj, Operator Frame for End ∗ A(H), J. Linear Topol. Algebra, 8 (2019), 85-95.
  13. M. Rossafi, S. Kabbaj, ∗-K-g-Frames in Hilbert A-Modules, J. Linear Topol. Algebra, 7 (2018), 63-71.
  14. M. Rossafi, S. Kabbaj, ∗-G-Frames in Tensor Products of Hilbert C∗-Modules, Ann. Univ. Paedagog. Crac. Stud. Math. 17 (2018), 17-25. https://doi.org/10.2478/aupcsm-2018-0002.
  15. M. Rossafi, S. Kabbaj, Generalized Frames for B(H, K), Iran. J. Math. Sci. Inf. accepted.