Redundancy of Fusion frames

In this manuscript, we introduce the notion of redundancy of fusion frames, which is concerned with the properties of lower and upper redundancies. This motivates a carefully chosen list of desired properties for upper and lower redundancies. The means to achieve this properties is to consider the minimum and maximum values of the redundancy function which is dened on the unit sphere of the Hilbert space and measures the concentration of subspaces around each point. In addition, the range of values that the redundancies assume is characterized.