A note on the groups of finite type and the Hartman–Mycielski construction
Volume 164 / 2021
Colloquium Mathematicum 164 (2021), 171-174
MSC: Primary 22A10; Secondary 46L10.
DOI: 10.4064/cm8285-6-2020
Published online: 31 August 2020
Abstract
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.
