Abstract

W. Sun in his paper [W. Sun, G-frames and g-Riesz bases. J. Math. Anal. Appl 322 (2006),437-452] has introduced $g$-frames which are generalized frames and cover many recent generalizations of frames such as bounded quasi-projections, fusion frames and pseudo-frames. We give a necessary and sufficient condition for a $g$-frame to be a dual to a given $g$-frame and obtain some sufficient conditions under which sequences are stable under small perturbations.

Keywords and Phrases

G-frames, dual $g$-frames, orthogonal $g$-frames, $g$-R-dual sequence.

A.M.S. subject classification

42C15.

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