Abstract

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CONTINUOUS P-FRAMES AND THEIR PERTURBATION IN BANACH SPACES

E. Osgooei


— Replacing the sequence of vectors with a net indexed by an ordered set where the set is endowed with a measure space, we obtain a generalization of discrete frames which is called continuous p-frames. The problem of combining the synthesis and analysis operators of these frames is solved in this paper. We also prove that a perturbation of a weakly measurable function G of a cp-frame F is again a cp-frame when there is a small enough gap between F and G