Birkhoff's theorem and multidimensional numerical range
Spectral Theory
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0110131,
title = {Birkhoff's theorem and multidimensional numerical range},
author = {Yuri Safarov},
journal= {arXiv preprint arXiv:math/0110131},
year = {2007}
}
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35 pages