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Characterization of sequences of frame norms
-
Marcin Bownik
und
John Jasper
Veröffentlicht/Copyright:
1. März 2011
Abstract
We show that frames with frame bounds A and B are images of orthonormal bases under positive operators with spectrum contained in 
. Then, we give an explicit characterization of the diagonals of such operators, which in turn gives a characterization of the sequences which are the norms of a frame. Our result extends the tight case result of Kadison [Proc. Natl. Acad. Sci. USA 99: 4178–4184, 2002], [Proc. Natl. Acad. Sci. USA 99: 5217–5222, 2002], which characterizes diagonals of orthogonal projections, to a non-tight case. We illustrate our main theorem by studying the set of possible lower bounds of positive operators with prescribed diagonal.
Received: 2009-04-22
Revised: 2010-01-29
Published Online: 2011-03-01
Published in Print: 2011-May
© Walter de Gruyter Berlin · New York 2011
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