Stability of g-Frame Expansions

In this paper we investigate the stability of onesided perturbation to gframe expansions. We show that if Lambda is a gframe of a Hilbert space mathcal{H}, Lambda_{i}^{a}=Lambda_{i}+Theta_{i} where Theta_{i} in mathcal{L}(mathcal{H},mathcal{H}_{i}), and widetilde{f}=sum_{i in J}Lambda_{i}^{star}widetilde{Lambda}_{i}^{a}f, widehat{f}=sum_{i in J}(Lambda_{i}^{a})^{star}widetilde{Lambda_{i}}f, then |widehat{f}f|leq alpha |f| and |fwidetilde{f}|leq beta |f| for some alpha and beta.