A Note on the Carath\'{e}odory Number of the Joint Numerical Range
Functional Analysis
2024-09-10 v1
Abstract
We show that the Carath\'{e}odory number of the joint numerical range of many bounded self-adjoint operators is at most , and even at most if the underlying Hilbert space has dimension at least . This extension of the classical convexity results for numerical ranges shows that also joint numerical ranges are significantly less non-convex than general sets.
Cite
@article{arxiv.2409.04444,
title = {A Note on the Carath\'{e}odory Number of the Joint Numerical Range},
author = {Beatrice Maier and Tim Netzer},
journal= {arXiv preprint arXiv:2409.04444},
year = {2024}
}