Abstract
The construction of Parseval frames with special, rigid geometric properties has left many open problems even after decades of efforts. The construction of similar types of fusion frames is even less developed. We construct a large family of equi-isoclinic Parseval fusion frames by taking the Naimark complement of the union of orthonormal bases. If these bases are chosen to be mutually unbiased, then the resulting fusion frame subspaces are spanned by mutually unbiased basic sequences. By giving an explicit representation for Naimark complements, we are able to construct concrete fusion frames in their respective Hilbert spaces.
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