论文标题
阿尔伯蒂 - 乌尔曼（Uhlmann
Alberti--Uhlmann problem on Hardy--Littlewood--Pólya majorization
论文作者
论文摘要
我们充分描述了与半五届von neumann代数相关的非交换$ l_1 $空间中自动化元素的双随机轨道，该空间与1980年代艾尔伯蒂（Alberti）和乌尔曼（Uhlmann）提出的问题回答了文献中的几个结果。 It follows further from our methods that, for any $σ$-finite von Neumann algebra $\mathcal{M}$ equipped a semifinite infinite faithful normal trace $τ$, there exists a self-adjoint operator $y\in L_1(\mathcal{M},τ)$ such that the doubly stochastic orbit of $y$ does not coincide with the orbit从Hardy-Littlewood-Pólya的意义上讲，$ Y $的$ $，这证实了Hiai的猜想。但是，我们表明Hiai的猜想因非$σ$ -finite von Neumann代数而失败。本文的主要结果还回答了1960年代由于卢森堡和RYFF引起的（非共同的）无限问题。
We fully describe the doubly stochastic orbit of a self-adjoint element in the noncommutative $L_1$-space affiliated with a semifinite von Neumann algebra, which answers a problem posed by Alberti and Uhlmann in the 1980s, extending several results in the literature. It follows further from our methods that, for any $σ$-finite von Neumann algebra $\mathcal{M}$ equipped a semifinite infinite faithful normal trace $τ$, there exists a self-adjoint operator $y\in L_1(\mathcal{M},τ)$ such that the doubly stochastic orbit of $y$ does not coincide with the orbit of $y$ in the sense of Hardy--Littlewood--Pólya, which confirms a conjecture by Hiai. However, we show that Hiai's conjecture fails for non-$σ$-finite von Neumann algebras. The main result of the present paper also answers the (noncommutative) infinite counterparts of problems due to Luxemburg and Ryff in the 1960s.
