A Note on the Carath\'{e}odory Number of the Joint Numerical Range
A Note on the Carath\'{e}odory Number of the Joint Numerical Range
We show that the Carath\'{e}odory number of the joint numerical range of $d$ many bounded self-adjoint operators is at most $d-1$, and even at most $d-2$ if the underlying Hilbert space has dimension at least $3$. This extension of the classical convexity results for numerical ranges shows that also joint …