Complex Free Spectrahedra, Absolute Extreme Points, and Dilations
Functional Analysis
2022-09-12 v2 Operator Algebras
Abstract
Evert and Helton proved that real free spectrahedra are the matrix convex hulls of their absolute extreme points. However, this result does not extend to complex free spectrahedra, and we examine multiple ways in which the analogous result can fail. We also develop some local techniques to determine when matrix convex sets are not (duals of) free spectrahedra, as part of a continued study of minimal and maximal matrix convex sets and operator systems. These results apply to both the real and complex cases.
Keywords
Cite
@article{arxiv.2108.09185,
title = {Complex Free Spectrahedra, Absolute Extreme Points, and Dilations},
author = {Benjamin Passer},
journal= {arXiv preprint arXiv:2108.09185},
year = {2022}
}
Comments
21 pages. To appear in Documenta Mathematica