Birkhoff's theorem and multidimensional numerical range

Yuri Safarov

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arXiv · math/0110131

Birkhoff's theorem and multidimensional numerical range

Yuri Safarov

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Abstract

We study the relation between the spectrum of a self-adjoint operator and its multidimensional numerical range. It turns out that the multidimensional numerical range is a convex set whose extreme points are sequences of eigenvalues of the operator. Every collection of eigenvalues which can be obtained by the Rayleigh--Ritz formula generates an extreme point of the multidimensional numerical range. However, it may also have other extreme points.

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BibTeX RIS

Yuri Safarov. 2005-12-19. Birkhoff's theorem and multidimensional numerical range. https://arxiv.org/abs/math/0110131

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