On \(^*\)-fusion frames for Hilbert \(C^*\)-modules

Abstract

Our paper aims to extend fusion frames to Hilbert C\(^{*}\)-modules. We introduce \(^*\)-fusion frames associated to weighted sequences of closed orthogonally complemented submodules, showcasing similarities to Hilbert space frames. Using Dragan S. Djordjevic’s distance, we define submodule angles and establish a new topology on the set of sequences of closed orthogonally complemented submodules. Relying on this topology, we obtain for our \(^*\)-fusion frames, some new perturbation results of topological and geometric character.