PreprintCC BY 4.0arXiv
Sufficient positive maps between von Neumann algebras: Rényi divergences
Abstract
We prove recovery theorems for α-z Rényi divergences under normal unital positive maps between von Neumann algebras. Previous results in this setting required 2-positivity, while recent finite dimensional work showed that this assumption can be relaxed to mere positivity. Our proof uses sufficiency for JW*-subalgebras and Lp-spaces over them to characterize equality in the data processing inequality. As a further application of our methods, we solve a problem discussed by Haagerup and Stormer: Every conditional expectation of a von Neumann algebra onto a JW*-subalgebra factors through a conditional expectation onto the generated von Neumann subalgebra.
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BibTeX
@misc{jencova2026sufficient,
title = {{Sufficient positive maps between von Neumann algebras: Rényi divergences}},
author = {Anna Jenčová and Lauritz van Luijk},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28510},
eprint = {2608.28510},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28510},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sufficient positive maps between von Neumann algebras: Rényi divergences
AU - Anna Jenčová
AU - Lauritz van Luijk
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28510
UR - https://arxiv.org/abs/2608.28510
AB - We prove recovery theorems for α-z Rényi divergences under normal unital positive maps between von Neumann algebras. Previous results in this setting required 2-positivity, while recent finite dimensional work showed that this assumption can be relaxed to mere positivity. Our proof uses sufficiency for JW*-subalgebras and L^p-spaces over them to characterize equality in the data processing inequality. As a further application of our methods, we solve a problem discussed by Haagerup and Stormer: Every conditional expectation of a von Neumann algebra onto a JW*-subalgebra factors through a conditional expectation onto the generated von Neumann subalgebra.
ER -