Open Access

# $g$-frames and stability of $g$-frames in Hilbert spaces

### Abstract

Wenchang Sun in his paper [Wenchang Sun, $G$-frames and $g$-Riesz bases, J. Math. Anal. Appl. 322 (2006), 437-452] has introduced $g$-frames which are generalized frames and include ordinary frames and many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. In this paper we develop the $g$-frame theory for separable Hilbert spaces and give characterizations of $g$-frames and we show that $g$-frames share many useful properties with frames. We present a version of the Paley-Wiener Theorem for $g$-frames which is in spirit close to results for frames, due to Ole Christensen.

### Article Information

 Title $g$-frames and stability of $g$-frames in Hilbert spaces Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 3, 271-286 MathSciNet MR2458491 Copyright The Author(s) 2008 (CC BY-SA)

### Authors Information

Abbas Najati
Faculty of Sciences, Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Islamic Republic of Iran

M. H. Faroughi
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Islamic Republic of Iran

Asghar Rahimi
Department of Mathematics, University of Maragheh, Maragheh, Islamic Republic of Iran

### Citation Example

Abbas Najati, M. H. Faroughi, and Asghar Rahimi, $g$-frames and stability of $g$-frames in Hilbert spaces, Methods Funct. Anal. Topology 14 (2008), no. 3, 271-286.

### BibTex

@article {MFAT437,
AUTHOR = {Najati, Abbas and Faroughi, M. H. and Rahimi, Asghar},
TITLE = {$g$-frames and stability of $g$-frames in Hilbert spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {3},
PAGES = {271-286},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=437},
}