Stability of Frames in Quaternionic Hilbert Spaces

Abstract

In this article, we study various types of perturbations of frames in quaternionic Hilbert spaces. We shall study perturbation of a frame by a non-zero quaternion, perturbation by a sequence in the space itself, and perturbation by a positively confined sequence of real numbers. Examples are given to justify this study. Finally, we obtain various sufficient conditions for the stability of frames under such perturbations.