Some Generalizations of Relay Fusion Frames and F ,

Abstract

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 $C^{\ast }$ -modules very naturally and shift some common attributes of fusion frames and relay fusion frames in Hilbert spaces to relay fusion frames in Hilbert $C^{\ast }$ -modules. In addition, we generalize some perturbation results in frame theory to relay fusion frames in Hilbert $C^{\ast }$ -modules. Finally, we introduce a class of $\left(F,G\right)$ -relay fusion frames as a generalization of $K$ -frames and present some perturbation results for $\left(F,G\right)$ -relay fusion frames in Hilbert $C^{\ast }$ -modules.