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arXiv · 1104.0810

Every Hilbert space frame has a Naimark complement

Peter G. Casazza·Matt Fickus·Dustin Mixon·Jess Peterson·Ihar Smalyanau
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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.

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Peter G. Casazza, Matt Fickus, Dustin Mixon, Jess Peterson, Ihar Smalyanau. 2011-04-05. Every Hilbert space frame has a Naimark complement. https://arxiv.org/abs/1104.0810

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