Year: 2026
Type: preprint
Abstract: Let $\mathcal M$ be a semifinite von Neumann algebra equipped with a semifinite faithful normal trace $τ$. We establish Jensen's trace inequality in full generality and characterize its equality case, which answers two questions raised in [Kosaki2013] and [HaradaKosaki2008]. As an application, we derive noncommutative Lamperti-type inequalities and their equality conditions. Employing this result, we characterize linear isometries (not necessarily surjective) on a class of $F$-normed noncommutative Orlicz spaces, which provides a noncommutative Lamperti's theorem for linear isometries.
Source: arXiv (Cornell University)
Authors: Fang, Kai, He, Xin, Huang, Jinghao
Institutions: Harbin Institute of Technology, Harbin Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204882348