Reduction of joint c-numerical ranges

摘要

Let (H1,H2,…,Hm) be an m-tuple of n-by-n Hermitian matrices and c∈Rn. We investigate the reduction problem of the joint c-numerical range Wc(H1,H2,…,Hm). In particular, for m=3 and n⩾3, we prove that Wc(H1,H2,H3) is attainable by the joint numerical range W(K1,K2,K3) for some triple Hermitian matrices (K1,K2,K3).