G- FRAMES AND THEIR STABILITY IN HILBERT SPACE

K. N. Rajeswari; Neelam George

doi:10.56827/SEAJMMS.2022.1802.12

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

DOI: https://doi.org/10.56827/SEAJMMS.2022.1802.12

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 quasiprojections, 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.