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arXiv · 2608.30172

Jensen' s trace inequality with equality condition and noncommutative Lamperti's theorem

Kai Fang·Xin He·Jinghao Huang
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Abstract

Let $\mathcal M$ be a semifinite von Neumann algebra equipped with a semifinite faithful normal trace $\tau$. 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.

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Kai Fang, Xin He, Jinghao Huang. 2026-08-31. Jensen' s trace inequality with equality condition and noncommutative Lamperti's theorem. https://arxiv.org/abs/2608.30172

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