Some Generalizations of Relay Fusion Frames and F,G-Relay Fusion Frames in Hilbert C∗-Modules - Xiujiao Chi; Guoqing Hong; Pengtong Li (Journal of Mathematics)
The relay fusion frame proposed by Hong and Li is an extension of a fusion frame that has many applications in science. In this study, we introduce relay fusion frames in Hilbert C∗-modules very naturally and shift some common attributes of fusion frames and relay fusion frames in Hilbert spaces to relay fusion frames in Hilbert C∗-modules. In addition, we generalize some perturbation results in frame theory to relay fusion frames in Hilbert C∗-modules. Finally, we introduce a class of F,G-relay fusion frames as a generalization of K-frames and present some perturbation results for F,G-relay fusion frames in Hilbert C∗-modules.