Journal of Mathematical Physics, Analysis, Geometry
2019, vol. 15, No 3, pp. 395-411   https://doi.org/10.15407/mag15.03.395     ( to contents , go back )
https://doi.org/10.15407/mag15.03.395

Frames in Quaternionic Hilbert Spaces

Sumit Kumar Sharma

Kirori Mal College, University of Delhi, Delhi-110007, India
E-mail: sumitkumarsharma@gmail.com

Shashank Goel

Amity Institute of Applied Sciences, Amity University, Noida, U.P-201301, India
E-mail: sgoel54@amity.edu

Received January 4, 2018, revised March 3, 2018.

Abstract

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.

Mathematics Subject Classification 2000: 42C15, 42A38.
Key words: frame, quaternionic Hilbert spaces.

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