Geodesic
On the generalized Riesz-dual sequences in Hilbert spaces
Eurasian mathematical journal, Tome 8 (2017) no. 4, pp. 45-54.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we define the generalized Riesz-dual sequence from a g-Bessel sequence with respect to a pair of g-orthonormal bases as a generalization of the Riesz-dual sequence. We characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract g-frame setting. 
@article{EMJ_2017_8_4_a5,
     author = {F. Enayati and M. S. Asgari},
     title = {On the generalized {Riesz-dual} sequences in {Hilbert} spaces},
     journal = {Eurasian mathematical journal},
     pages = {45--54},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a5/}
}
TY  - JOUR
AU  - F. Enayati
AU  - M. S. Asgari
TI  - On the generalized Riesz-dual sequences in Hilbert spaces
JO  - Eurasian mathematical journal
PY  - 2017
SP  - 45
EP  - 54
VL  - 8
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a5/
LA  - en
ID  - EMJ_2017_8_4_a5
ER  - 
%0 Journal Article
%A F. Enayati
%A M. S. Asgari
%T On the generalized Riesz-dual sequences in Hilbert spaces
%J Eurasian mathematical journal
%D 2017
%P 45-54
%V 8
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a5/
%G en
%F EMJ_2017_8_4_a5
F. Enayati; M. S. Asgari. On the generalized Riesz-dual sequences in Hilbert spaces. Eurasian mathematical journal, Tome 8 (2017) no. 4, pp. 45-54. http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a5/

[1] M.S. Asgari, “Operator-valued bases on Hilbert spaces”, J. Linear and Topological Algebra, 2:4 (2013), 201–218

[2] M.S. Asgari, H. Rahimi, “Generalized frames for operators in Hilbert spaces”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 17:2 (2014), 1450013, 20 pp. | DOI | MR

[3] P.G. Casazza, G. Kutyniok, “Frames of subspaces”, Wavelets, Frames and Operator Theory (College Park, MD, 2003), Contemp. Math., 345, Amer. Math. Soc., 2004, 87–113 | DOI | MR

[4] P.G. Casazza, G. Kutyniok, M.C. Lammers, “Duality principles in frame theory”, J. Fourier Anal. Appl., 10 (2004), 383–408 | DOI | MR

[5] O. Christensen, An introduction to frames and Riesz bases, Springer, Switzerland, 2016 | MR

[6] O. Christensen, H.O. Kim, R.Y. Kim, “On the duality principle by Casazza, Kutyniok, and Lammers”, J. Fourier Anal. Appl., 17 (2011), 640–655 | DOI | MR

[7] O. Christensen, X.C. Xiao, Y.C. Zhu, “Characterizing R-duality in Banach spaces”, Acta Mathematica Sinica, Eng. Series, 29:1 (2013), 75–84 | DOI | MR

[8] X. Guo, “G-bases in Hilbert spaces”, Abstract and Applied Analysis, 2012, 923729, 14 pages pp. | DOI | MR

[9] X. Guo, “Operator parameterizations of g-frames”, Taiwanese J. Math., 18:1 (2014), 313–328 | DOI | MR

[10] A. Najati, A. Rahimi, “Generalized frames in Hilbert spaces”, Bull. Iranian Math. Soc., 35:1 (2009), 97–109 | MR

[11] D.T. Stoeva, O. Christensen, “On R-Duals and the Duality Principle in Gabor Analysis”, J. Fourier Anal. Appl., 21:2 (2015), 383–400 | DOI | MR

[12] W. Sun, “G-frames and g-Riesz bases”, J. Math. Anal. Appl., 322 (2006), 437–452 | DOI | MR

[13] W. Sun, “Stability of g-frames”, J. Math. Anal. Appl., 326 (2007), 858–868 | DOI | MR

[14] X.M. Xian, Y.C. Zhu, “Duality principles of frames in Banach spaces”, Acta Math. Sci. Ser. A Chin. Ed., 29:1 (2009), 94–102 | MR