标题： 连续选择 II$_1$因子中的酉元 显示英文标题

标题： Continuous Selection of Unitaries in II$_1$ Factors

摘要： 我们证明了连续值类比于这样一个基本事实：II$_1$因子中的投影的Murray-von Neumann子等价性完全由迹值评估决定。此外，我们还利用这个结果解决了因子平凡的$W^\ast$-丛的迹问题，其中底空间的覆盖维数最多为1。我们的论证基于Michael的一个连续选择定理在von Neumann代数上的应用。 显示英文摘要

摘要： We prove continuous-valued analogues of the basic fact that Murray-von Neumann subequivalence of projections in II$_1$ factors is completely determined by tracial evaluations. We moreover use this result to solve the so-called trace problem in the case of factorial trivial $W^\ast$-bundles whose base space has covering dimension at most 1. Our arguments are based on applications of a continuous selection theorem due to Michael to von Neumann algebras.