Duals and approximate duals of g-frames in Hilbert spaces

Journal of Linear and Topological Algebra

مقاله 11، دوره 04، شماره 04، اسفند 2015، صفحه 259-265   

نوع مقاله: Research Paper

نویسندگان

M. Mirzaee Azandaryani^{* 1}؛ A. Khosravi²

¹Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

²Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran

چکیده

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.

کلیدواژه‌ها

Frame؛ g-frame؛ duality؛ approximate duality

مراجع

[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.