DUALITY OF OPERATOR FRAMES IN BANACH SPACES

In this paper, approximate dual operator frames in separable Banach spaces are introduced. The relationship between the duality of p-frames and the duality of (p,Y)operator frames is characterized. The perturbations of dual operator frames and approximate dual operator frames are discussed. With approximate dual operator frames, we can approximatively reconstruct, or almost reconstruct the elements of Banach spaces. For a (p,Y)-operator frame, a sequence of approximate dual operator frames that converges to the dual operator frame always exists. We show that the direct sum of (p,Y)-operator frames can preserve the actual and approximate duality of operator frames.