Numerical ranges encircled by analytic curves

2020/03/11 by Lins, Brian
#47A12 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2003.05347

Abstract

Let D be a bounded convex domain in ℂ with a regular analytic boundary. Suppose that the numerical range W(A) of a bounded linear operator A is contained in D. If W(A) intersects the boundary ∂ D at infinitely many points while the essential numerical range W_ess(A) does not intersect ∂ D, then W(A) = D. This generalizes some infinite dimensional analogues of a result of Anderson.

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