Some Results on Perturbation of Duality of OPV-Frames
DOI:
https://doi.org/10.52737/18291163-2024.16.6-1-13Keywords:
Frames, Operator Valued Frames, Perturbation of FramesAbstract
In this paper, we consider a perturbation of operator-valued frames (OPV-frames) and obtain conditions for their stability in terms of operators associated with the OPV-frames. Also, some duality relations of OPV-frames are discussed. Finally, some properties of the duals of OPV-frames are proven.
References
R. Bhardwaj, S.K. Sharma and S.K. Kaushik, Trace class operators via OPV-frames. Filomat, 35 (2021), no. 13, pp. 4353-4368. https://doi.org/10.2298/fil2113353b DOI: https://doi.org/10.2298/FIL2113353B
R. Calderbank, P.G. Casazza, A. Heinecke, G. Kutyniok and A. Pezeshki, Sparse fusion frames: existence and construction. Adv. Comput. Math., 35 (2011), pp. 1-31. https://doi.org/10.1007/s10444-010-9162-3 DOI: https://doi.org/10.1007/s10444-010-9162-3
P.G. Cazassa and O. Christensen, Perturbation of operators and applications to frame theory. J. Fourier Anal. Appl., 3 (1997), no. 5, pp. 543-557. https://doi.org/10.1007/bf02648883 DOI: https://doi.org/10.1007/BF02648883
P.G. Cazassa, G. Kutyniok and S. Li, Fusion frames and distributed processing. Appl. Comput. Harmon. Anal., 25 (2008), no. 1, pp. 114-132. DOI: https://doi.org/10.1016/j.acha.2007.10.001
O. Christensen, An introduction to Frames and Riesz Bases. Second Edition. Boston, Birkhäuser, 2016. DOI: https://doi.org/10.1007/978-3-319-25613-9
I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions. J. Math. Phy., 27 (1986), no. 5, pp. 1271-1283. https://doi.org/10.1063/1.527388 DOI: https://doi.org/10.1063/1.527388
R.J. Duffin and A.C. Schaeffer, A class of nonharmonic Fourier series. Trans. Am. Math. Soc., 72 (1952), no. 2, pp. 341-366. https://doi.org/10.1090/s0002-9947-1952-0047179-6 DOI: https://doi.org/10.1090/S0002-9947-1952-0047179-6
P. Gavruta, On the duality of fusion frames. J. Math. Anal. and Appl., 333 (2007), no 2, pp. 871-879. DOI: https://doi.org/10.1016/j.jmaa.2006.11.052
L. Gavruta, Frames for operators. Appl. Comput. Harmon. Anal., 32 (2012), no. 1, pp. 139-144. DOI: https://doi.org/10.1016/j.acha.2011.07.006
L. Gavruta and P. Gavruta, Some properties of operator-valued frames. Acta Math. Sci., 36 (2016), no. 2, pp. 469-476. DOI: https://doi.org/10.1016/S0252-9602(16)30013-3
D. Han, P.T. Li, B. Meng and W. Tang, Operator-valued frames and structured quantum channels. Sci. China Math., 54 (2011), no 11, pp. 2361-2372. https://doi.org/10.1007/s11425-011-4292-8 DOI: https://doi.org/10.1007/s11425-011-4292-8
A. Jamioikowski, An Introduction to frames and their applications to quantum optics. Quantum Bio-Informatics III (2010), pp. 147-154. DOI: https://doi.org/10.1142/9789814304061_0013
V. Kaftal, L. David and S. Zhang, Operator-valued frames. Trans. Am. Math. Soc., 361 (2009), no. 12, pp. 6349-6385. https://doi.org/10.1090/s0002-9947-09-04915-0 DOI: https://doi.org/10.1090/S0002-9947-09-04915-0
S.K. Kaushik, A generalization of frames in Banach spaces. J. Contemp. Math. Anal., 44 (2009), pp. 212-218. https://doi.org/10.3103/s1068362309040025 DOI: https://doi.org/10.3103/S1068362309040025
S.K. Kaushik, A note on exact Banach frames. Int. J. Pure Appl. Math., 31 (2006), no. 2, pp. 279-286.
S.K. Kaushik, Some results concerning frames in Banach spaces. Tamking J. Math., 38 (2007), no. 3, pp. 267-276. https://doi.org/10.5556/j.tkjm.38.2007.80 DOI: https://doi.org/10.5556/j.tkjm.38.2007.80
K.T. Poumai and S.K. Kaushik, Wavelet frames in $L^2(R^d)$. Rocky Mountain J. Math., 50 (2020), no. 2, pp. 677-692. https://doi.org/10.1216/rmj.2020.50.677 DOI: https://doi.org/10.1216/rmj.2020.50.677
K.T. Poumai, S.K. Kaushik and S.V. Djordjevic, Operator valued frames and applications to quantum channels. In: International Conference on Sampling Theory and Applications (SampTA), IEEE, 2017, pp. 217-221. https://doi.org/10.1109/sampta.2017.8024361 DOI: https://doi.org/10.1109/SAMPTA.2017.8024361
R. Sharma, Some properties of OPV-frames. Poincare J. Anal. Appl., 10 (2023), no. 1, pp. 215-224. https://doi.org/10.46753/pjaa.2023.v010i01.015 DOI: https://doi.org/10.46753/pjaa.2023.v010i01.015
W. Sun, G-frames and g-Riesz bases. J. Math. Anal. Appl., 322 (2006), no. 1, pp. 437-452. DOI: https://doi.org/10.1016/j.jmaa.2005.09.039
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Armenian Journal of Mathematics
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
