2018/01/14 by Victor Kaftal, Kaftal, Victor, David Larson +1
Mathematics · #46C05 (Secondary) #47A53 (primary) #47B15 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46C05 #msc:47A53 #msc:47B15
paper · pdf · doi:10.48550/arxiv.1801.04509
arxiv created 2018/01/14 · arxiv updated 2018/01/16
A sequence of scalars is said to be admissible for a positive operator A on a Hilbert space if it is the diagonal of VAV* for some partial isometry V having as domain the closure of the range of A. When A is a projection, the celebrated Kadison's carpenter theorem provides a sufficient condition for a sequence to be admissible for A. We prove that the same condition is sufficient for the sequence to be admissible for A when A is a sum of projections (converging in the SOT). This provides an independent proof of Kadison's carpenter theorem.