Corners of multidimensional numerical ranges
Stanislav Anatol'evich Shkarin · arXiv (Cornell University) · 2009
The $n$-dimensional numerical range of a densely defined linear operator $T$ on a complex Hilbert space $\H$ is the set of vectors in $\C^n$ of the form $(,...,)$, where $e_1,...,e_n$ is an orthonormal system in $\H$, consisting of vectors from the domain of $T$. We prove that the components of every corner point of the $n$-dimensional numerical range are eigenvalues of $T$.