TY - JOUR ID - 123060 TI - The correspondence of Fusion frames and frames In Hilbert $C^*$-modules and finite Gabor Fusion frames JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Kamyabi-Gol, Rajab Ali AU - Mohammadpour, Mozhgan AD - Ferdowsi University of Mashhad AD - Department of Pure Mathematics, Faculty of Mathematical sciences, Ferdowsi University of Mashhad, Iran Y1 - 2021 PY - 2021 VL - 7 IS - 2 SP - 187 EP - 200 KW - fusion frame KW - frames in Hilbert $C^*$-modules KW - fusion Riesz basis KW - time frequency representation KW - Gabor fusion frame DO - 10.22034/kjm.2020.169670.1308 N2 - 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. UR - https://www.kjm-math.org/article_123060.html L1 - https://www.kjm-math.org/article_123060_549a8420805639b552b28a7afb2b87be.pdf ER -