Abstract
In this paper, we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames in Hilbert spaces. Moreover, we define the related operators of c-K-g-frames. Then, we give necessary and sufficient conditions on c-K-g-frames to characterize them. Finally, we verify the perturbation of c-K-g-frames.
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Abdollahpour, M.R., Faroughi, M.H.: Continuous G-frames in Hilbert spaces. Southeast Asian Bull. Math. 32, 1–19 (2008)
Ali, S.T., Antoine, J.P., Gazeau, J.P.: Continuous frames in Hilbert spaces. Ann. Phys. 222, 1–37 (1993)
Asgari, M.S., Rahimi, H.: Generalized frames for operators in Hilbert spaces. Inf. Dimens. Anal. Quant. Probab. Relat. Top. 17(2), 1450013 (2014)
Balazs, P., Bayer, D., Rahimi, A.: Multipliers for countinuous frames in Hilbert spaces. J. Phys. A Math. Theor. 45, 2240023(20p) (2012)
Casazza, P.G., Christensen, O.: Perturbation of operators and application to frame theory. J. Fourier Anal. Appl. 3, 543–557 (1997)
Douglas, R.G.: No majorization, factorization and range inclusion of operators on Hilbert space. Proc. Am. Math. Soc. 17(2), 413–415 (1966)
Duffin, R.J., Schaeffer, A.C.: A class of nonharmonic Fourier series. Trans. Am. Math. Soc. 72, 341–366 (1952)
Fornasier, M., Rauhut, H.: Continuous frames, function spaces, and the discretization problem. J. Fourier Anal. Appl. 11(3), 245–287 (2015)
Gabardo, J.P., Han, D.: Frames associated with measurable space. Adv. Comput. Math. 18(3), 127–147 (2003)
Gavruta, L.: Frames for operators. Appl. Comput. Harmon. Anal. 32, 139–144 (2012)
Hua, D., Hung, Y.: K-g-frames and stability of K-g-frames in Hilbert spaces. J. Korean Math. Soc. 53(6), 1331–1345 (2016)
Kaiser, G.: A Friendly Guide to Wavelets. Birkhauser, Boston (1994)
Li, D.-F., Yang, L.-J., Wu, G.: The unified condition for stability of g-frames. In: 2010 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE), 2010 , Vol. 4, pp. V4-305–V4-308
Najati, A., Faroughi, M.H., Rahimi, A.: G-frames and stability of g-frames in Hilbert spaces. Methods. Funct. Anal. Topol. 14(3), 271–286 (2008)
Rahmani, M.: On some properties of c-frames. J. Math. Res. Appl. 37(4), 466–476 (2017)
Rahmani, M.: Sum of c-frames, c-Riesz Bases and orthonormal mappings. U. P. B. Sci. Bull Ser. A 77(3), 3–14 (2015)
Rahimi, A., Najati, A., Dehghan, Y.N.: Continuous frames in Hilbert spaces. Methods. Funct. Anal. Topol. 12(2), 170–182 (2006)
Strohmer, T., Heath Jr., R.: Grassmannian frames with applications to conding and communications. Apple. Comput. Harmon. Anal. 14, 257–275 (2003)
Sun, W.C.: G-frames and g-Riesz. J. Math. Anal. Appl. 322(1), 437–452 (2006)
Xiao, X., Zhu, Y.: Exact K-g-frames in Hilbert spaces. Results Math. 72, 1329–1339 (2017)
Sun, W.: Stability of g-frame. J. Math. Anal. Appl. 326(2), 858–868 (2007)
Zhou, Y., Zhu, Y.: K-g-frames and dual g-frames for closed subspaces. Acta Math. Sin. Chin. Ser. 56(5), 799–806 (2013)
Zhou, Y., Zhu, Y.: Characterization of K-g-frames in Hilbert spaces. Acta Math. Sin. Chin. Ser. 57(5), 1031–1040 (2014)
Acknowledgements
The authors would like to thank Professor M. H. Faroughi for his comments and suggestions. We express also our special thanks to the reviewers due to their helpful comments for improving paper.
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Communicated by Ali Ghaffari.
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Alizadeh, E., Rahimi, A., Osgooei, E. et al. Continuous K-g-Frames in Hilbert Spaces. Bull. Iran. Math. Soc. 45, 1091–1104 (2019). https://doi.org/10.1007/s41980-018-0186-7
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DOI: https://doi.org/10.1007/s41980-018-0186-7