Strict convexity of the joint c-numerical range
Copyright policy )Strict convexity of the joint c-numerical range
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.
- Soochow University Taiwan
- Hirosaki University Japan
Numerical Analysis, Algebra and Number Theory, joint \(c\)-numerical range, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, strictly convex set, Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.), Geometry and Topology, weakly strictly hyperbolic form, convex hull
Numerical Analysis, Algebra and Number Theory, joint \(c\)-numerical range, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, strictly convex set, Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.), Geometry and Topology, weakly strictly hyperbolic form, convex hull
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