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Jensen' s trace inequality with equality condition and noncommutative Lamperti's theorem
Abstract
Let 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.
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BibTeX
@misc{fang2026jensen,
title = {{Jensen' s trace inequality with equality condition and noncommutative Lamperti's theorem}},
author = {Kai Fang and Xin He and Jinghao Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.30172},
eprint = {2608.30172},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30172},
}
RIS
TY - UNPB
TI - Jensen' s trace inequality with equality condition and noncommutative Lamperti's theorem
AU - Kai Fang
AU - Xin He
AU - Jinghao Huang
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2608.30172
UR - https://arxiv.org/abs/2608.30172
AB - Let 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.
ER -