BIFRAMES AND THEIR PROPERTIES IN QUATERNIONIC HILBERT SPACES

Nitin Sharma (Department of Mathematics, Maitreyi College, University of Delhi, India)
Amita Aggarwal (Department of Mathematics, Hansraj College, University of Delhi, India)
Raksha Sharma (Department of Physics, Kirori Mal College, University of Delhi, India)

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application

In this paper, we focus on defining and analyzing biframes within quaternionic Hilbert spaces, thereby extending the study of biframes beyond the complex Hilbert space framework. We establish that frames can be viewed as a specific instance of biframes. Moreover, we introduce the concept of biframe operators and utilize it to derive a reconstruction formula. Several characterization results pertaining to biframes are also discussed. Additionally, the conditions under which the image of a biframe under a bounded linear operator continues to retain the biframe structure are examined.