Every Hilbert space frame has a Naimark complement

2011/04/05 by Peter G. Casazza, Casazza, Peter G., Matt Fickus +7 · 2 citations
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1104.0810

Changes after Refereeing

arxiv created 2013/04/22 · arxiv updated 2013/04/23

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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