Mirzaee Azandaryani, M., Khosravi, A. (2016). Duals and approximate duals of g-frames in Hilbert spaces. Journal of Linear and Topological Algebra (JLTA), 04(04), 259-265.
M. Mirzaee Azandaryani; A. Khosravi. "Duals and approximate duals of g-frames in Hilbert spaces". Journal of Linear and Topological Algebra (JLTA), 04, 04, 2016, 259-265.
Mirzaee Azandaryani, M., Khosravi, A. (2016). 'Duals and approximate duals of g-frames in Hilbert spaces', Journal of Linear and Topological Algebra (JLTA), 04(04), pp. 259-265.
Mirzaee Azandaryani, M., Khosravi, A. Duals and approximate duals of g-frames in Hilbert spaces. Journal of Linear and Topological Algebra (JLTA), 2016; 04(04): 259-265.
Duals and approximate duals of g-frames in Hilbert spaces
1Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran
2Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
Abstract
In this paper we get some results and applications for duals and approximate duals of g-frames in Hilbert spaces. In particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of Hilbert spaces. We also obtain some results for perturbations of approximate duals.
[1] O. Christensen, R. S. Laugesen, Approximate dual frames in Hilbert spaces and applications to Gabor frames, Sampl. Theory Signal Image Process. 9 (2011), 77-90.
[2] I. Daubechies, A. Grossmann and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 27 (1986), 1271-1283.
[3] R. J. Duffin, A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341-366.
4] A. Khosravi, M. Mirzaee Azandaryani, Approximate duality of g-frames in Hilbert spaces, Acta Mathematica Scientia. 34B(3) (2014), 639-652.
[5] A. Khosravi, M. Mirzaee Azandaryani, G-frames and direct sums, Bull. Malays. Math. Sci. Soc. 36(2) (2013), 313-323.
[6] A. Khosravi, M. Mirzaee Azandaryani, Fusion frames and g-frames in tensor product and direct sum of Hilbert spaces, Appl. Anal. Discrete Math. 6 (2012), 287-303.
[7] A. Khosravi, K. Musazadeh, Fusion frames and g-frames, J. Math. Anal. Appl. 342 (2008), 1068-1083.
[8] G. J. Murphy, C∗-Algebras and Operator Theory. Academic Press, San Diego, 1990.
[9] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322 (2006), 437-452.
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