Constructing relay fusion frames in Hilbert spaces

In this work, we start by introducing a general methodology to generate new relay fusion frames from given ones, namely the Spatial Complement Method, and analyze the relationships between the parameters of the original and the new relay fusion frame. We then present another simple approach to obtain relay fusion frames by considering fusion frames for its components. An explicit characterization concerning the existence of Parseval relay fusion frame consisting of two initial subspaces is given. Moreover, we obtain a necessary and sufficient condition under which the spatial complements of alternate dual relay fusion frames remain to be alternate dual relay fusion frames. Some results about Bessel relay fusion sequences are included. Finally, several examples are also given.