Joint k-numerical ranges of operators

Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal Projections

“…It is known that W(T) is a nonempty bounded convex set in the complex plane C and its closure, denoted by W(T), always contains the spectrum σ(T) of T (see [1,2]). In addition, for T 1 , T 2 ∈ B(H), we have W(T 1 ⊕ T 2 ) � conv(W(T 1 ) ∪ W(T 2 )), where conv(S) stands for the convex hull of the set S. For references on the numerical range and its generalizations, see, for instance, [3][4][5][6][7][8].…”