Frames in quaternionic Hilbert spaces

In this paper, we introduce and study the frames in separable quaternionic Hilbert spaces. The results on the existence of frames in quaternionic Hilbert spaces and a characterization of frames in quaternionic Hilbert spaces in terms of frame operator are given. Finally, a Paley–Wiener type perturbation result for the frames in a quaternionic Hilbert space has been obtained.