Some properties of K-Operator Frame in Hilbert $C^{\ast}$-modules

Authors

  • Roumaissae Eljazzar
  • Mohamed Rossafi Faculty of Sciences, Dhar El Mahraz University Sidi Mohamed Ben Abdellah, Fes,
  • Mohammed Klilou

DOI:

https://doi.org/10.20956/j.v18i3.20459

Keywords:

$K$-Operator Frame, Dual $K$-operator frame, $C^{\ast}$-algebra, Hilbert $C^{\ast}$-modules, Tensor Product

Abstract

In this paper, we present some properties of K-operator Frame in Hilbert $C^{\ast}$-modules.Topics that will be discussed include: K-operator Frame and Dual K-operator frame in Hilbert $C^{\ast}$-modules.We will also study K-operator Frame in two Hilbert $C^{\ast}$-modules with different $C^{\ast}$-algebras.

Downloads

Download data is not yet available.

References

bibitem{Ali} A. Alijani, M. A. Dehghan, $ast$-frames in Hilbert $mathcal{C}^{ast}$-modules, {it U.P.B. Sci. Bull., Ser. A}, {bf 73}(4) (2011), 89-106.

bibitem{Ch} O. Christensen, An Introduction to Frames and Riesz bases, {it Brikhauser}, 2016.

bibitem{Con} J. B. Conway, A Course In Operator Theory, {it AMS}, {bf 21}, 2000.

bibitem{Dav} F. R. Davidson, $mathcal{C}^{ast}$-algebra by example, {it Fields Ins. Monog.} 1996.

bibitem{Gras} I. Daubechies, A. Grasmann and Y. Meyer, Painless nonorthogonal expansions, {it J. Math. Phys.} {bf 27} (1986), 1271-1283.

bibitem{Duf} R. J. Duffin and A. C. Schaeffer, A class of nonharmonic fourier series, {it Trans. Amer. Math. Soc.} {bf 72} (1952),

-366.

bibitem{KabbRoss} S. Kabbaj, M. Rossafi, $ast$-Operator frame for $End_{mathcal{A}}^{ast}(mathcal{H})$, Wavelets and Linear Algebra 5(2) (2018), 1–13. https://doi.org/10.22072/WALA.2018.79871.1153

bibitem{BA} A. Khosravi, B. Khosravi, Frames and bases in tensor products of Hilbert spaces and Hilbert $mathcal{C}^{ast}$-modules,

{it Proc. Indian Acad. Sci. Math. Sci.} {bf 117} (2007), 1-12.

bibitem{Lan} E.C. Lance, Hilbert C*-modules, A Toolkit for Operator Algebraists, {it University of Leeds, Cambridge University Press}, 1995.

bibitem{RK2019} M. Rossafi, S. Kabbaj, Operator frame for $End_{mathcal{A}}^{ast}(mathcal{H})$, Journal of Linear and Topological

Algebras 8(2) (2019), 85–95.

bibitem{Ros} M. Rossafi, S. Kabbaj, emph{K-operator Frame for $End_{mathcal{A}}^{ast}(mathcal{H})$}, Asia Mathematika Volume 2, Issue 2, (2018), 52-60.

bibitem{RK2018} M. Rossafi, S. Kabbaj, $ast$-K-operator frame for $End_{mathcal{A}}^{ast}(mathcal{H})$, Asian-Eur. J. Math. 13(3) (2020),

Paper ID 2050060, 11 pages. https://doi.org/10.1142/S1793557120500606

bibitem{Rochka} M. Rossafi, F. Chouchene,

S. Kabbaj, Integral frame in Hilbert $mathcal{C}^{ast}$-module, arXiv

preprint-arXiv:2005.09995v2 [math.FA] 30 Nov 2020.

bibitem{RK2021} M. Rossafi, S. Kabbaj, Some Generalizations of Frames in Hilbert Modules, International Journal of Mathematics and Mathematical Sciences, vol. 2021, Article ID 5522671, 11 pages, 2021. https://doi.org/10.1155/2021/5522671

bibitem{Lil} A. Ljiljana,

On frames for countably generated Hilbert $C^{ast}-modules$

Proceedings of the American Mathematical Society.

Vol. 135 ,(2007),

-478.

bibitem{Doug} Z. Lun Chuan, The factor decomposition theorem of bounded generalized inverse modules and their topological continuity. Acta Mathematica Sinica, 2007, Vol. 23, 1413-1418.

Downloads

Published

2022-05-15

Issue

Section

Research Articles