Controlled pg-frames in Hilbert spaces
محورهای موضوعی : Abstract harmonic analysis
1 - Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran
کلید واژه: Hilbert space, Controlled frame, pg-frame,
چکیده مقاله :
In this paper, for extending the concepts of $p$-frame and controlled frame for Hilbert spaces, we will introduce the concept of controlled $pg$-frames in Hilbert spaces. Then, we present characterizations of controlled $pg$-frames and some results of frames in the view of controlled $pg$-frames.
[1] M. R. Abdollahpour, M. H. Faroughi, A. Rahimi, pg-frames in Banach spaces, Methods of Func. Anal. Top. 13 (3) (2007), 201-210.
[2] C. D. Aliprantis, K. C. Border, Infinite Dimensional Analysis, A Hitchhikers Guide, Springer-Verlag, New York-Berlin, 1999.
[3] M. S. Asgari, G. Kavian, Expansion of Bessel and g-Bessel sequences to dual frames and dual g-frames, J. Linear. Topological. Algebra. 2 (1) (2013), 51-57.
[4] P. Balazs, J. P. Antoine, A. Grybos, Wighted and controlled frames, Int. J. Wavelets, Multiresolut. Inf. Process. 8 (1) (2010), 109-132.
[5] B. G. Bodmann, V. I. Paulsenm, Frame paths and error bounds for sigma-delta quantization, Appl. Comput. Harmon. Anal. 22 (2007), 176-197.
[6] P. G. Casazza, Custom building finite frames wavelets, frames and operator theory, Contemp. Math. 345 (2004), 61-86.
[7] P. G. Casazza, Modern tools for WeylHeisenberg (Gabor) frame theory, Adv. Imaging. Electron. Phys. 115 (2001), 1-127.
[8] P. G. Casazza, G. Kutyniok, Frames of subspaces, wavelets, frames and operator theory, Contemp. Math. 345 (2004), 87-113.
[9] R. J. Duffin, A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341-366.
[10] D. Hua, Y. Huang, Controlled K-g-frames in Hilbert spaces, Results. Math. 72 (3) (2017), 1227-1238.
[11] H. Heuser, Functional Analysis, John Wiley, New York, 1982.
[12] M. Mirzaee Azandaryani, A. Khosravi, Duals and approximate duals of g-frames in Hilbert spaces, J. Linear. Topological. Algebra. 4 (4) (2015), 259-265.
[13] G. J. Murphy, C∗-algebras and operator theory, Academic Press, London, 1990.
[14] W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl. 322 (1) (2006), 437-452.
[15] X. Xiao, Y. Zhu, L. Gavruta, Some properties of K-frames in Hilbert spaces, Results Math. 63 (3-4) (2013), 1243-1255.
