Characterization of Approximate Dual g-frame

Constructing approximate dual frames is much easier than constructing classical dual frames, and approximate dual frames derive an almost same perfect reconstruction formula as classical dual frames. In this paper, under the background of subspace frames (fusion frames), an explicit characterization of approximate dual g-frames was obtained. As an application, we prove that for a given pair of approximate dual g-frames (Λ_nn, Γ_nn), there existed another pair of approximate dual g-frames (Ψ_nn, Υ_nn) such that T_ΛU_Γ=T_ΨU_Υ, where T_Y and U_Y denote the pre-frame and analysis operators of the g-frame Y_nn.