Every Hilbert Space Frame has a Naimark Complement

Authors

Peter G. Casazza, University of Missouri
Matthew C. Fickus, Air Force Institute of TechnologyFollow
Dustin G. Mixon, Princeton University
Jesse D. Peterson, University of Missouri
Ihar Smalyanau, University of Missouri

Document Type

Article

Publication Date

10-1-2013

Abstract

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.

Comments

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Previous version (e-print): arxiv:1104.0810 [math.FA]. . Date of arXiv submission, 5 Apr 2011, last updated 22 Apr 2013.

DOI

10.1016/j.jmaa.2013.04.047

Source Publication

Journal of Mathematical Analysis and Applications

Recommended Citation

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