Some Generalizations of Relay Fusion Frames and $\left(F,G\right)$-Relay Fusion Frames in Hilbert $$

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 ∗ -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.