关于有限型群与Hartman-Mycielski构造的注记
A note on the groups of finite type and the Hartman-Mycielski construction
摘要：
Ando、Matsuzawa、Thom和Törnquist解决了Sorin Popa的一个问题，他们构造了一个波兰的酉算子群的例子，这个群具有强算子拓扑，它的左和右一致结构重合，但不嵌入有限冯诺依曼代数的酉群。问题仍然是这样一个群体是否能够联系起来。在这里，我们观察到一个连通的（事实上，同胚的希尔伯特空间）的例子是从上述作者的例子通过哈特曼-Mycielski建设。
英文摘要：
Ando, Matsuzawa, Thom, and Törnquist have resolved a problem by Sorin Popa by constructing an example of a Polish group of unitary operators with the strong operator topology, whose left and right uniform structures coincide, but which does not embed into the unitary group of a finite von Neumann algebra. The question remained whether such a group can be connected. Here we observe that a connected (in fact, homeomorphic to the Hilbert space) example is obtained from the example of the above authors via the Hartman--Mycielski construction.
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