The correspondence of Fusion frames and frames In Hilbert $C^*$-modules and finite Gabor Fusion frames

Document Type : Original Article


1 Ferdowsi University of Mashhad

2 Department of Pure Mathematics, Faculty of Mathematical sciences, Ferdowsi University of Mashhad, Iran



In this paper, we show that fusion frames in the finite dimensional Hilbert space $H$ correspond to frames in the Hilbert $C^*$-module $\mathcal{B}\left(\mathbb{C}^n\right)$. Moreover, we show that every tight fusion frame and Reisz fusion basis in $\mathbb{C}^n$ correspond to a tight frame and Reisz basis in the Hilbert $C^*$-module $\mathcal{B}\left(\mathbb{C}^n\right)$ respectively. Then, we use this fact to characterize the dual of Reisz fusion basis. Finally, we introduce Gabor fusion frames as a new notion.