AI 中文总结
本文针对II₁因子间的次迹完全正映射，刻画其在不可约II₁子因子酉元共轭下的扁平化性质，以Pimsner-Popa型不等式的失效为精确阻碍，推广了Popa的渐近正交化结果。
AI 中文摘要
设M是一个II₁因子，N是一个迹冯·诺依曼代数，Φ: M→N是一个次迹完全正映射。对于M中不可约的II₁子因子P，我们刻画了Φ在被P中的酉元共轭时展现扁平化性质的条件。具体来说，我们证明了E_P∘Φ*∘Φ不满足Pimsner-Popa型不等式是该性质的精确阻碍，等价于自然关联的P-N双模的左弱混合。作为应用，我们得到了推广Popa结果的渐近正交化结论。
英文摘要
Let $M$ be a $\mathrm{II}_1$ factor, $N$ a tracial von Neumann algebra, and $Φ: M \rightarrow N$ a subtracial completely positive map. For an irreducible $\mathrm{II}_1$ subfactor $P \subseteq M$, we characterize when $Φ$ exhibits a flattening property under conjugation by unitaries in $P$. To be specific, we show that the failure of a Pimsner-Popa type inequality for $E_P \circ Φ^* \circ Φ$ is the precise obstruction, equivalently characterized by left weak mixing of a naturally associated $P$-$N$ bimodule. As an application, we obtain an asymptotic orthogonalization result generalizing a result of Popa.
Comments15 pages, v2: Minor revisions and improvements in exposition and references
