On Weaving Fusion Frames for Hilbert Spaces

Very recently Bemrose et al. introduced a new concept of 'weaving frames' in separable Hilbert spaces. Two frames {φi}iϵI and {ψi}iϵI for a separable Hilbert space H are said to be woven, if there are universal positive constants A and B such that for every subset σ ⊂ I, the family {φi}iϵσ ∪ {ψi}iϵσc is a frame for H with lower and upper frame bounds A and B, respectively. Weaving frames and fusion frames are connected with pre-processing and distributed data processing in signal analysis. In this paper, we present sufficient conditions for weaving fusion frames in separable Hilbert spaces. Paley-Wiener type perturbation results for weaving fusion frames are also given.