Let be the algebra of all bounded linear operators on a complex Hilbert space , and let be a norm ideal in . For , define the elementary operator on by (). The aim of this paper is to give necessary and sufficient conditions under which the equality holds. Here and denote the algebraic numerical range and spatial numerical range of an operator , respectively, and denotes the closed convex hull of a subset .
"A note concerning the numerical range of a basic elementary operator." Ann. Funct. Anal. 7 (3) 434 - 441, August 2016. https://doi.org/10.1215/20088752-3605510