Erasures and Equalities for Fusion Frames in Hilbert Spaces

Fusion frames are widely studied recently due to its many kinds of applications. In this paper we focus on the erasure of a fusion frame; we use a bounded linear operator to equivalently characterize a given fusion frame to be robust to an erasure of any numbers of elements; it turns out that our result is more general and covers some important results previously obtained by Asgari, Casazza, and Kutyniok. We also present a more general equality result for any fusion frame (not restricted to be tight), which improves the fusion version of a theorem obtained by Li and Sun.