G- FRAMES AND THEIR STABILITY IN HILBERT SPACE

Authors

  • K. N. Rajeswari (School of Mathematics, D. A. V. V., Indore - 452001, Madhya Pradesh, INDIA)
  • Neelam George (School of Mathematics, D. A. V. V., Indore - 452001, Madhya Pradesh, INDIA)

Keywords:

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

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.

 

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Published

2023-06-21

Issue

Vol. 18 No. 02 (2022): South East Asian Journal of Mathematics and Mathematical Sciences

Section

Articles