CONICET | Buscador de Institutos y Recursos Humanos

A new notion of dual fusion frame has been recently introduced bythe authors. In this article that notion is further motivated and itis shown that it is suitable to deal with questions posed in afinite-dimensional real or complex Hilbert space, reinforcing theidea that this concept of duality solves the question about anappropriate definition of dual fusion frames. It is shown that forovercomplete fusion frames there always exist duals different fromthe canonical one. Conditions that assure the uniqueness of dualsare given. The relation of dual fusion frame systems with dualframes and dual projective reconstruction systems is established.Optimal dual fusion frames for the reconstruction in case oferasures of subspaces, and optimal dual fusion frame systems for thereconstruction in case of erasures of local frame vectors aredetermined. Examples that illustrate the obtained results areexhibited.