Corners of multidimensional numerical ranges

Details Corners of multidimensional numerical ranges Corners of multidimensional numerical ranges

2009-03-02

arxiv.org/abs/0903.0269v1

Mathematics

Functional Analysis

Scientific paper

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 $(< Te_1,e_1>,...,< Te_n,e_n>)$, 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 $T$.

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