Some identities and inequalities for g-fusion frames
Problemy analiza, Tome 9 (2020) no. 2, pp. 152-162.

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

G-fusion frames, which are obtained from the combination of g-frames and fusion frames, were recently introduced for Hilbert spaces. In this paper, we present a new identity for g-frames, which was given by Najati for a special case. Also, by using the idea of this identity and the dual frames, some equalities and inequalities are presented for g-fusion frames.
Keywords: g-frame, dual g-frame, g-fusion frame, dual g-fusion frame.
@article{PA_2020_9_2_a9,
     author = {R. Zarghami Farfar and V. Sadri and R. Ahmadi},
     title = {Some identities and inequalities for g-fusion frames},
     journal = {Problemy analiza},
     pages = {152--162},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2020_9_2_a9/}
}
TY  - JOUR
AU  - R. Zarghami Farfar
AU  - V. Sadri
AU  - R. Ahmadi
TI  - Some identities and inequalities for g-fusion frames
JO  - Problemy analiza
PY  - 2020
SP  - 152
EP  - 162
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2020_9_2_a9/
LA  - en
ID  - PA_2020_9_2_a9
ER  - 
%0 Journal Article
%A R. Zarghami Farfar
%A V. Sadri
%A R. Ahmadi
%T Some identities and inequalities for g-fusion frames
%J Problemy analiza
%D 2020
%P 152-162
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2020_9_2_a9/
%G en
%F PA_2020_9_2_a9
R. Zarghami Farfar; V. Sadri; R. Ahmadi. Some identities and inequalities for g-fusion frames. Problemy analiza, Tome 9 (2020) no. 2, pp. 152-162. http://geodesic.mathdoc.fr/item/PA_2020_9_2_a9/

[1] Arabyani F., Minaei G. M., Anjidani E., “On Some Equalities and Inequalities for $K$-Frames”, Indian J. Pure. Appl. Math., 50:2 (2019), 297–308 | DOI | MR

[2] Balan R., Casazza P. G., Edidin D., Kutyniok G., “A New Identity for Parseval Frames”, Proc. Amer. Math. Soc., 135 (2007), 1007–1015 | DOI | MR | Zbl

[3] Blocsli H., Hlawatsch H. F., Fichtinger H. G., “Frame-Theoretic analysis of oversampled filter bank”, IEEE Trans. Signal Processing, 46:12 (1998), 3256–3268 | DOI

[4] Candes E. J., Donoho D. L., “New tight frames of curvelets and optimal representation of objects with piecewise $C^2$ singularities”, Comm. Pure and App. Math., 57:2 (2004), 219–266 | DOI | MR | Zbl

[5] Casazza P. G., Christensen O., “Perturbation of Operators and Application to Frame Theory”, J. Fourier Anal. Appl., 3 (1997), 543–557 | DOI | MR | Zbl

[6] Casazza P. G., Kutyniok G., “Frames of Subspaces”, Contemp. Math., 345, 1998, 87–114 | DOI | MR

[7] Casazza P. G., Kutyniok G., Li S., “Fusion Frames and distributed processing”, Appl. comput. Harmon. Anal., 57:2 (2004), 219–266 ; 25:1 (2008), 114–132 | MR | DOI | Zbl

[8] Christensen O., An Introduction to Frames and Riesz Bases, Birkhäuser, 2016 | MR | Zbl

[9] Diestel J., Sequences and series in Banach spaces, Springer-Verlag, New York, 1984 | MR

[10] Duffin R. J., Schaeffer A. C., “A class of nonharmonic Fourier series”, Trans. Amer. Math. Soc., 72:1 (1952), 341–366 | DOI | MR | Zbl

[11] Faroughi M. H., Ahmadi R., “Some Properties of C-Frames of Subspaces”, J. Nonlinear Sci. Appl., 1:3 (2008), 155–168 | DOI | MR | Zbl

[12] Feichtinger H. G., Werther T., “Atomic Systems for Subspaces”, Proceedings SampTA (Orlando, FL, 2001), 163–165 | MR

[13] Găvruţa P., “On the duality of fusion frames”, J. Math. Anal. Appl., 333 (2007), 871–879 | DOI | MR

[14] Hansen F., Pečarić J., Perić I., “Jensens Operator inequality and its converses”, Math. Scand., 100 (2007), 61–73 | DOI | MR | Zbl

[15] Heuser H., Functional Analysis, John Wiley, New York, 1991 | MR

[16] Kadison R., Singer I., “Extensions of pure states”, American Journal of Math., 81 (1959), 383–400 | DOI | MR | Zbl

[17] Khayyami M., Nazari A., “Construction of Continuous g-Frames and Continuous Fusion Frames”, Sahand Comm. Math. Anal., 4:1 (2016), 43–55 | Zbl

[18] Li D., Leng J., “On Some New Inequalities for Fusion Frames in Hilbert Spaces”, Math. Ineq. Appl., 20:3 (2017), 889–900 | DOI | MR | Zbl

[19] Matković M., Pečarić J., Perić I., “A variant of Jensen's Inequality of Mercer's Type For Operators with Applications”, Linear Algebra Appl., 418 (2006), 551–564 | DOI | MR | Zbl

[20] Najati A., Faroughi M. H., Rahimi A., “g-frames and stability of g-frames in Hilbert spaces”, Methods of Functional Analysis and Topology, 14:3 (2008), 305–324 | MR

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

[22] Sadri V., Rahimlou G., Ahmadi R., Zarghami Farfar R., “Construction of g-fusion frames in Hilbert spaces”, Inf. Dim. Anal. Quan. Prob. (IDA-QP), 2019 (to appear) | MR

[23] Sun W., “G-Frames and G-Riesz bases”, J. Math. Anal. Appl., 326 (2006), 437–452 | DOI | MR