Admissible sequences for positive operators
Operator Algebras
2018-01-16 v1
Abstract
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.
Cite
@article{arxiv.1801.04509,
title = {Admissible sequences for positive operators},
author = {Victor Kaftal and David Larson},
journal= {arXiv preprint arXiv:1801.04509},
year = {2018}
}