Every Hilbert space frame has a Naimark complement

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 actually all Hilbert space frames have Naimark complements which possess all the usual properties for Naimark complements of Parseval frames with one notable exception. Thus these complements can be used with regard to equiangular frames, the restricted isometry 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.