Some Properties of Controlled K-g-Frames in Hilbert C∗-Modules

Main Article Content

Rachid Echarghaoui, M'hamed Ghiati, Mohammed Mouniane, Mohamed Rossafi

Abstract

This paper is devoted to studying the controlled K-g-frames in Hilbert C∗-modules, some useful results are presented. Also, the concept of controlled K-g-dual frames is given. Finally, we discuss the stability problem for controlled K-g-frames in Hilbert C∗-modules.

Article Details

References

  1. P. Balazs, J.-P. Antoine, A. Gryboś, Weighted and Controlled Frames: Mutual Relationship and First Numerical Properties, Int. J. Wavelets Multiresolut Inf. Process. 08 (2010), 109–132. https://doi.org/10.1142/S0219691310003377.
  2. R.J. Duffin, A.C. Schaeffer, a Class of Nonharmonic Fourier Series, Trans. Amer. Math. Soc. 72 (1952), 341-366.
  3. M. Frank, D.R. Larson, A-Module Frame Concept For Hilbert C ∗ -Modules, Funct. Harmonic Anal. Wavelets Contempt. Math. 247 (2000), 207-233.
  4. D. Gabor, Theory of Communication, J. Inst. Elect. Eng. 93 (1946), 429–457.
  5. M. Ghiati, S. Kabbaj, H. Labrigui, A. Touri, M. Rossafi, ∗-K-g-frames and their duals for Hilbert A-modules, J. Math. Comput. Sci. 12 (2022), 5. https://doi.org/10.28919/jmcs/6819.
  6. S. Kabbaj, M. Rossafi, ∗-operator Frame for End ∗ A(H), Wavelet Linear Algebra, 5 (2018), 1-13.
  7. A. Khosravi, B. Khosravi, Fusion Frames and G-Frames in Hilbert C*-Modules, Int. J. Wavelets Multiresolut. Inform. Process. 06 (2008), 433–446. https://doi.org/10.1142/S0219691308002458.
  8. M. Rashidi-Kouchi, A. Rahimi, On controlled frames in Hilbert C*-modules, Int. J. Wavelets Multiresolut. Inform. Process. 15 (2017), 1750038. https://doi.org/10.1142/S0219691317500382.
  9. F. D. 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.
  10. W. L. Paschke, Inner Product Modules over B ∗ -Algebras, Trans. Am. Math. Soc. 182 (1973), 443–468. https://doi.org/10.1090/S0002-9947-1973-0355613-0.
  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. Inform. accepted.
  16. X.C. Xiao, X.M. Zeng, Some Properties of g-frames in Hilbert C ∗ -Modules, J. Math. Anal. Appl. 363 (2010), 399–408. https://doi.org/10.1016/j.jmaa.2009.08.043.
  17. Q. Xu, L. Sheng, Positive Semi-Definite Matrices of Adjointable Operators on Hilbert C*-Modules, Linear Algebra Appl. 428 (2008), 992–1000. https://doi.org/10.1016/j.laa.2007.08.035.
  18. L.C. Zhang, The Factor Decomposition Theorem of Bounded Generalized Inverse Modules and Their Topological Continuity, Acta Math. Sinica. 23 (2007), 1413–1418. https://doi.org/10.1007/s10114-007-0867-2.