Abstract
Let beta(H) be the algebra of all bounded linear operators on a complex Hilbert space H, and let S be a norm ideal in beta(H). For A, B epsilon beta(H), define the elementary operator M-S,M-A,M-B on S by M-S,M-A,M-B(X) = AXB (X epsilon S). The aim of this paper is to give necessary and sufficient conditions under which the equality V(M-S,M-A,M-B) - (co) over bar (W(A)W(B)) holds. Here V(T) and W(T) denote the algebraic numerical range and spatial numerical range of an operator T, respectively, and (co) over bar(Omega) denotes the closed convex hull of a subset Omega subset of C.