2004/11/19 by Jorge Antezana, Antezana, Jorge, Pedro Massey +3 · 1 citation
Computer Science · Mathematics · #46L05 (Secondary) #47A63 (Primary) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L05 #msc:47A63
paper · pdf · doi:10.48550/arxiv.math/0411442
arxiv created 2004/11/19 · openalex publication_date 2004/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a C^*-algebra and ϕ:\cA→ L(H) be a positive unital map. Then, for a convex function f:I→ ℝ defined on some open interval and a self-adjoint element a∈ A whose spectrum lies in I, we obtain a Jensen's-type inequality f(ϕ(a)) ≤ ϕ(f(a)) where ≤ denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered i.e., operator convex, monotone convex and arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered.