A note on the boundary of the joint numerical range
Jor-Ting Chan · Linear and Multilinear Algebra · 2017
Let H be a complex Hilbert space and let A=(A1,…,An) be an n-tuple of self-adjoint operators on H. The joint numerical range of A is the setW(A)={(⟨A1x,x⟩,…,⟨Anx,x⟩):xis a unit vector inH}.By a result of Li and Poon, the closure of W(A), denoted by W(A)-, is star-shaped with each point in the joint essential numerical range of A a star centre. In this note, we give a few observations about the boundary of W(A) and W(A)- basing on their results.