A note on the groups of finite type and the Hartman-Mycielski construction

Vladimir Pestov

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arXiv · 2005.02522

A note on the groups of finite type and the Hartman-Mycielski construction

Vladimir Pestov

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Abstract

Ando, Matsuzawa, Thom, and T\"ornquist 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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Vladimir Pestov. 2020-05-05. A note on the groups of finite type and the Hartman-Mycielski construction. https://arxiv.org/abs/2005.02522

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