A non-commutative F&M Riesz Theorem
Operator Algebras
2022-01-20 v1 Functional Analysis
Abstract
We extend results on analytic complex measures on the complex unit circle to a non-commutative multivariate setting. Identifying continuous linear functionals on a certain self-adjoint subspace of the Cuntz--Toeplitz algebra, the free disk operator system, with non-commutative (NC) analogues of complex measures, we refine a previously developed Lebesgue decomposition for positive NC measures to establish an NC version of the Frigyes and Marcel Riesz Theorem for `analytic' measures, i.e. complex measures with vanishing positive moments. The proof relies on novel results on the order properties of positive NC measures that we develop and extend from classical measure theory.
Cite
@article{arxiv.2201.07393,
title = {A non-commutative F&M Riesz Theorem},
author = {Michael T. Jury and Robert T. W. Martin and Edward J. Timko},
journal= {arXiv preprint arXiv:2201.07393},
year = {2022}
}
Comments
29 page