Every Hilbert Space Frame has a Naimark Complement
Naimark complements for Hilbert space Parseval frames are one of the most fundamental and useful results in the field of frame theory. We will show that actually all Hilbert space frames have Naimark complements which possess all the usual properties for Naimark complements with one notable exception. So these complements can be used for equiangular frames, RIP property, fusion frames etc. Along the way, we will correct a mistake in a recent fusion frame paper where chordal distances for Naimark complements are computed incorrectly.
Journal of Mathematical Analysis and Applications
Casazza, P. G., Fickus, M., Mixon, D. G., Peterson, J., & Smalyanau, I. (2013). Every Hilbert space frame has a Naimark complement. Journal of Mathematical Analysis and Applications, 406(1), 111–119. https://doi.org/10.1016/j.jmaa.2013.04.047