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arXiv · 0903.0269

Corners of multidimensional numerical ranges

S. Shkarin
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Abstract

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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S. Shkarin. 2009-03-02. Corners of multidimensional numerical ranges. https://arxiv.org/abs/0903.0269

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