Corners of multidimensional numerical ranges

The $n$-dimensional numerical range of a densely defined linear operator $T$ on a complex Hilbert space \H is the set of vectors in ${\text{C}}^n$ of the form $(< Te_1,e_1>,…,< Te_n,e_n>)$,where$e_1,…,e_n$isanorthonormalsystemin$\H$,consistingofvectorsfromthedomainof$T$. We prove that the components of every corner point of the $n$-dimensional numerical range are eigenvalues of $T$.