冯·诺依曼代数间的充分正映射：Rényi散度
Sufficient positive maps between von Neumann algebras: Rényi divergences
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中文总结 AI 辅助
该研究针对冯·诺依曼代数间的正规幺正正映射，证明了α-z Rényi散度的恢复定理，将此前所需的2-正性放宽至单纯正性，还解决了Haagerup与Stormer提出的条件期望分解问题。
中文摘要 AI 辅助
我们证明了冯·诺依曼代数间的正规幺正正映射下α-z Rényi散度的恢复定理。此前该场景下的结果要求2-正性，而近期有限维研究表明该假设可放宽至单纯正性。我们的证明利用了JW*-子代数的充分性及其上的L^p空间，以刻画数据处理不等式中的等式。作为方法的进一步应用，我们解决了Haagerup和Stormer讨论的问题：冯·诺依曼代数到JW*-子代数的每个条件期望，均可通过到生成的冯·诺依曼子代数的条件期望分解。
英文摘要
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.
