Document Type : Research Paper

Authors

1 Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.

3 Department of Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

Abstract

In this paper, we introduce the notion of woven g-fusion frames in Hilbert spaces. Then, we present sufficient conditions for woven g-fusion frames in terms of woven frames in Hilbert spaces. We extend some of the recent results of standard woven frames and woven fusion frames to woven g-fusion frames. Also, we study perturbations of woven g-fusion frames.

Keywords

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[1] M.S. Asgari and A. Khosravi, Frames and bases of subspaces in Hilbert spaces, J. Math. Anal. Appl., 308 (2005),pp. 541-553.
[2] T. Bemrose, P.G. Casazza, K. Grochenig, M.C. Lammers and R.G. Lynch, Weaving Frames, J. Oper. Matrices., 10 (2016), pp. 1093-1116.
[3] P.G. Casazza, D. Freeman and R.G. Lynch, Weaving Schauder frames, J. Approx. Theory., 211 (2016), pp. 42-60.
[4] P.G. Casazza and G. Kutyniok, Frames of Subspaces, Contemp Math. Amer. Math. Soc., 345, (2004), pp. 87-113.
[5] P.G. Casazza, G. Kutyniok and Sh. Li, Fusion frames and distributed processing, Appl. Comput. Harmon. Anal., 25 (2008), pp. 114-132.
[6] P.G. Casazza and R.G. Lynch, Weaving properties of Hilbert space frames, J. Proc. SampTA., (2015), pp. 110-114.
[7] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, Boston, (2016).
[8] I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys., 27 (1986), pp. 1271-1283.
[9] Deepshikha and L.K. Vashisht, Weaving K-frames in Hilbert spaces, Results Math., 73 (2018), pp. 1-20.
[10] R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72, (1952), pp. 341-366.
[11] D. Han and D. Larson, Frames, bases and group representations, Mem. Amer. Math. Soc., 147 (697) (2000).
[12] A. Khosravi and M.S. Asgari, Frames of subspaces and approximation of the inverse frame operator, Houston. J. Math., 33 (2007), pp. 907-920.
[13] A. Khosravi and K. Musazadeh, Fusion frames and g-frames, J. Math. Anal. Appl., 342 (2008), pp. 1068-1083.
[14] A. Khosravi and J. Sohrabi Banyarani, Weaving $g$-frames and weaving fusion frames, Bull. Malays. Math. Sci. Soc., 42 (2019), pp. 3111-3129.
[15] R. Rezapour, A. Rahimi, E. Osgooei and H. Dehghan, Controlled weaving frames in Hilbert spaces, Inf. Dim. Anal. Quan. Prob. Rel. Top., 22 (2019), pp. 1-18.
[16] V. Sadri,  Gh. Rahimlou, R. Ahmadi  and R. Zarghami Farfar,  Generalized Fusion Frames in Hilbert Spaces, Inf. Dim. Anal. Quan. Prob. Rel. Top., (to appear).
[17] W. Sun, g-frames and g-Riesz bases, J. Math. Anal. Appl., 322 (2006), pp. 437-452.
[18] L.K. Vashisht and Deepshikha, On continuous weaving frames, Adv. Pure Appl. Math., 8 (2017), pp. 15-31.
[19] L.K. Vashisht and Deepshikha, Weaving properties of generalized continuous frames generated by an iterated function system, J. Geom. Phys., 110 (2016), pp. 282-295.
[20] L.K. Vashisht and Deepshikha, S. Garg and G. Verma , On weaving fusion frames for Hilbert spaces, In: Proceedings of SampTA., (2017), pp. 381-385.