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Department of Mathematics,
Department of Mathematics,
University of California San Diego
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Math 243: Seminar in Functional Analysis
David Jekel
University of Copenhagen
The unitary group of a II1 factor is SOT-contractible
Abstract:
I show that the unitary group of any SOT-separable II_1 factor M, with the strong operator topology, is contractible. Combined with several old results, this implies that the same is true for any SOT-separable von Neumann algebra with no type I_n direct summands (n < infinity). The proof for the II_1-factor case uses regularization via free convolution and Popa's theorem on the existence of approximately free Haar unitaries in II_1 factors. I will also explain some of the bigger picture of the free probability ingredients.
October 28, 2025
11:00 AM
APM 6402
Research Areas
Functional Analysis / Operator Theory****************************
