Operators and dual frames in biframes

In recent decades, the frame theory and related topics have been attracted by many researchers. Biframe, a concept related to frames, was introduced as a pair of sequences, which dual frames are a particular case of them. In this article, more topics related to biframes are discussed. The effect of operators on biframes in order to preserve the biframe property is investigated more specifically. Then, by the importance of the relationship between a frame and its duals in the frame theory, this relationship is examined in the forming a biframe. In particular, the dual frames of two frames that form a biframe are studied, and interesting results are obtained.