Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reducing essential eigenvalues in the boundary of the numerical range   We examine a purely geometric property of a point in the boundary of the
numerical range of a (Hilbert space) operator that implies that such a point is
a reducing essential eigenvalue of the given operator. Roughly speaking, such a
property means that the boundary curve of the numerical range has infinite
curvature at that point (we must exclude however linear verteces because they
may be reducing eigenvalues without being reducing essential eigenvalues). This
result allows us to give an elegant proof of a conjecture of Joel Anderson:
{\it A compact perturbation of a scalar multiple of the identity operator can
not have the closure of its numerical range equal to half a disk (neither equal
to any acute circular sector).}

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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci