2015/12/17 by Mohsen Kian, Kian, Mohsen
Computer Science · Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #math.FA
paper · pdf · doi:10.48550/arxiv.1512.05529
to appear in "Quaestiones Mathematicae"
arxiv created 2015/12/17 · openalex publication_date 2015/12/17 · arxiv updated 2015/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that a real function f is convex if and only if the set E(f)=\(x,y)∈ℝ×ℝ; f(x)≤ y\, the epigraph of f is a convex set in ℝ2. We state an extension of this result for operator convex functions and C^*-convex sets as well as operator log-convex functions and C^*-log-convex sets. Moreover, the C^*-convex hull of a Hermitian matrix has been represented in terms of its eigenvalues.