Some properties of K-Operator Frame in Hilbert $C^{\ast}$-modules
DOI:
https://doi.org/10.20956/j.v18i3.20459Keywords:
$K$-Operator Frame, Dual $K$-operator frame, $C^{\ast}$-algebra, Hilbert $C^{\ast}$-modules, Tensor ProductAbstract
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.
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
Issue
Section
License
Copyright (c) 2022 Author and publisher
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license. This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.
