English

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)