Jensen's inequality for partial traces in von Neumann algebras
Operator Algebras
2026-03-11 v2 Classical Analysis and ODEs
Functional Analysis
Probability
Quantum Physics
Abstract
Motivated by a recent result on finite-dimensional Hilbert spaces, we prove a Jensen's inequality for partial traces in semifinite von Neumann algebras. We also prove a similar inequality in the framework of general (non-tracial) von Neumann algebras.
Keywords
Cite
@article{arxiv.2507.02422,
title = {Jensen's inequality for partial traces in von Neumann algebras},
author = {Mizanur Rahaman and Lyudmila Turowska},
journal= {arXiv preprint arXiv:2507.02422},
year = {2026}
}
Comments
Minor changes. Normality in lemma 5 and 6 are removed and a new Remark 2 has been added. To appear in the Bulletin of the London Mathematical Society (2026)