Noncommutative partially convex rational functions
Functional Analysis
2022-06-24 v4
Abstract
Motivated by classical notions of bilinear matrix inequalities (BMIs) and partial convexity, this article investigates partial convexity for noncommutative functions. It is shown that noncommutative rational functions that are partially convex admit novel butterfly-type realizations that necessitate square roots. The notion of xy-convexity, a strengthening of partial convexity arising in connection with BMIs, is also considered. A characterization of xy-convex polynomials is given.
Cite
@article{arxiv.2005.01086,
title = {Noncommutative partially convex rational functions},
author = {Michael Jury and Igor Klep and Mark E. Mancuso and Scott McCullough and James Eldred Pascoe},
journal= {arXiv preprint arXiv:2005.01086},
year = {2022}
}
Comments
This version [v4], corrected a typo in the proof of Proposition 4.7. The matrices X_0 and Y_0 are self-adjoint