Abstract:
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 (
Λnn,
Γnn), there existed another pair of approximate dual
g-frames (
Ψnn,
Υnn) such that
TΛUΓ=
TΨUΥ, where
TY and
UY denote the pre-frame and analysis operators of the
g-frame
Ynn.