[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2013.53.1.135

G-frames as Sums of Some g-orthonormal Bases

Abdollahpour, Mohammad Reza (Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili)
Najati, Abbas (Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili)

Publication Information

Kyungpook Mathematical Journal / v.53, no.1, 2013 , pp. 135-141 More about this Journal

Abstract

In this paper we show that a $g$ -frame for a Hilbert space $\mathcal{H}$ can be written as a linear combination of two $g$ -orthonormal bases for $\mathcal{H}$ if and only if it is a $g$ -Riesz basis for $\mathcal{H}$ . Also, we show that every $g$ -frame for a Hilbert space $\mathcal{H}$ is a multiple of a sum of three $g$ -orthonormal bases for $\mathcal{H}$ .

Keywords

g-Bessel sequence; g-frame; g-orthonormal basis; g-Riesz basis;

Citations & Related Records

Reference

1	P. G. Casazza, Every frames is a sum of three (but not two) orthonormal bases- and other frame representations, J. Fourier Anal. Appl., 4(1998), 727-732. DOI ScienceOn
2	P. G. Casazza and G. Kutyniok, Frames of subspaces, Contemp. Math., 345(2004), 87-113. DOI
3	O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, Boston, 2003.
4	O. Christensen and Y. C. Eldar, Oblique dual frames and shift invariant-spaces, Appl. Comput. Harmon. Anal., 17(2004), 48-68. DOI ScienceOn
5	R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72(1952), 341-366. DOI ScienceOn
6	M. Fornasier, Decompositions of Hibert space: local construction of global frames, Proc. Int. Conf. On Constructive Function Theory, varna(2002), B. Bojanov Ed., DARBA, Sofia, 2003, 275-281.
7	S. Li and H. Ogawa, Pseudoframes for subspaces with applications, J. Fourier Anal. Appl., 10(2004), 409-431. DOI ScienceOn
8	A. Najati, M. H. Faroughi and A. Rahimi, G-frames and stability of g-frames in Hilbert spaces, Methods Funct. Anal. Topology, 4(2008), 271-286.
9	S. Obeidat, S. Samarah, P. G. Casazza and J. C. Tremain, Sums of Hilbert Space frames, J. Math. Anal. Appl., 351(2009), 579-585. DOI ScienceOn
10	W. Sun, G-frames and g-Riesz bases, J. Math. Anal. Appl., 322(2006), 437-452. DOI ScienceOn