Sufficient positive maps between von Neumann algebras: Rényi divergences

• URL: http://arxiv.org/abs/2608.28510v1
• Date: Fri, 28 Aug 2026 16:43:20 GMT
• Title: Sufficient positive maps between von Neumann algebras: Rényi divergences
• Abstract summary: We prove recovery theorems for Rényi divergences under normal unital positive maps between von Neumann algebras.<n>Our proof uses sufficiency for JW*-subalgebras and $Lp$-spaces over them to characterize equality in the data processing inequality.
• Score: 1.4323566945483497
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $L^p$-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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