We define in a natural way the bicomplex analog of the frames (bc-frames) in the setting of  bicomplex infinite Hilbert spaces, and we characterize them in terms of their idempotent components. We also extend some classical results from frames theory to bc-frames and show that some of them do not remain valid for bc-frames in general. The construction of bc-frame operators and Weyl--Heisenberg bc-frames are also discussed.

In this paper, a new notion of frames is introduced: -operator frame as generalization of -frames in Hilbert C-modules introduced by A. Alijani and M. A. Dehghan [2] and we establish some results.

Abstract : In this paper, we investigate frames and g-frames and show that constructs the direct sum of frames for a finite number of frames. also, We show under what condition it becomes g-frames to T *−g-frames. Finally, we generalize Sun ’s theorem to Parseval frames.

In this paper, we present the concept of D􀀀, topological dual of a BC􀀀, module X with a D􀀀, norm k: kD, X and we , nd D􀀀, topological duals of D􀀀, normed bicomplex BC􀀀, modules l| p (BC) for 1 ,p < 1: We also investigate some fundamental topological properties of bicomplex BC􀀀, modules l| p (BC) by de, ning some topological concepts such as solid space, monotone space, BK􀀀, space, symmetric space in the bicomplex setting by using the D􀀀, norm j: j|:

Tight frames and g-frames are extremely useful in applications. A scalable frame was recentlyintroduced as a frame with the property of generating a tight frame by rescaling its frame vectors. In thispaper, we generalize this concept to g-frames, introduce scalable g-frames, obtain some characterizationsfor them, and demonstrate that scalability is stable under unitary operators and isomorophisms betweentwo Hilbert spaces. In addition, we consider Paley-Wiener perturbations of g-frames and achieve someresults regarding the preservation of their g-frame property.