Duality of g-Bessel sequences and some results about RIP g-‎frames

‎In this paper‎, ‎first we develop the duality concept for g-Bessel sequences‎ ‎and Bessel fusion sequences in Hilbert spaces‎. ‎We obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎We also expand every g-Bessel ‎sequence to a frame by summing some elements‎. ‎We define the restricted isometry property for ‎g-frames and generalize some results from (B‎. ‎G‎. ‎Bodmann et al‎, ‎Fusion frames and the restricted isometry property‎, ‎Num‎. ‎Func‎. ‎Anal‎. ‎Optim‎. ‎۳۳ (۲۰۱۲) ۷۷۰-۷۹۰) to g-frame situation‎. ‎Finally we study the stability of g-frames under erasure of ‎operators.‎

Keywords:

G-frames , Fusion frames , Dual frames , Pseudo-dual frames , Approximate dual frames , Bessel ‎sequences