Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Jenčová, Anna, van Luijk, Lauritz
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204786916