An observation concerning boundary points of the numerical range

Abstract

A theorem of H\"ubner states that non-round boundary points of the numerical range of a linear operator, i.e. points where the boundary has infinite curvature, are contained in the spectrum of the operator. In this note, answering a question of Salinas and Velasco, we will show that H\"ubner's result remains true under the weaker assumption that the boundary has infinite upper curvature. Our short and simple proof relies on some classical ideas of Berberian.