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

Authors

  • A. 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
  • A. Rahimi Department of Mathematics, University of Maragheh, Maragheh, Islamic Republic of Iran 

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Keywords:

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.

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Published

2008-09-25

Issue

Vol. 14 No. 3 (2008)

Section

Articles

How to Cite

Najati, A., et al. “$g$-Frames and Stability of $g$-Frames in Hilbert Spaces”. Methods of Functional Analysis and Topology, vol. 14, no. 3, Sept. 2008, pp. 271-86, https://zen.imath.kiev.ua/index.php/mfat/article/view/390.