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arXiv · 2608.28510

Sufficient positive maps between von Neumann algebras: R\'enyi divergences

Anna Jenčová·Lauritz van Luijk
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Abstract

We prove recovery theorems for $\alpha$-$z$ R\'enyi 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.

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Anna Jenčová, Lauritz van Luijk. 2026-08-28. Sufficient positive maps between von Neumann algebras: R\'enyi divergences. https://arxiv.org/abs/2608.28510

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