中文摘要：

近似对偶框架的构造比经典对偶框架的构造更为容易,而且可以导出几乎同样完美的重构公式,在子空间框架（fusion框架）的背景下,给出了近似对偶g-框架的明确刻画.作为应用,证明了对于给定的一组近似对偶g-框架（{Λ_n}_n,{Γ_n}_n）,存在另一组近似对偶框架（{Ψ_n}_n,{Υ_n}_n）,使得T_ΛU_Γ=T_ΨU_Υ,其中T_Y和U_Y分别表示g-框架{Y_n}_n的准框架算子与分析算子.

英文摘要：

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_n}_n,{ Γ_n}_n）,there existed another pair of approximate dual g-frames（ { Ψ_n}_n,{ Υ_n}_n） 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_n}_n.