Strict convexity of the joint \(c\)-numerical range (Q1931741)

Let \(H_{n}\) be the real vector space of \(n\times n\) complex Hermitian matrices. For any \(c=(c_{1},c_{2},\dots,c_{n})\in \mathbb R^{n}\) and an ordered \(m\)-tuple \(H=(H_{1},H_{2},\dots,H_{m})\in H_{n}^{m}\), the joint \(c\)-numerical range \(W_{c}(H)\) of \(H\) is defined. This paper investigates the outer boundary curve of the joint \(c\)-numerical range \(W_{c}(H_{1},H_{2},\dots,H_{m}) \), presents a sufficient condition for the outer boundary of the joint \(c\)-numerical range to contain no line segments, and discusses the strict convexity of the convex hull of the joint \(c\)-numerical range.