Reference : On continuity of measurable group representations and homomorphisms
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/26362
On continuity of measurable group representations and homomorphisms
English
Kuznetsova, Julia [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2012
Studia Mathematica
Polish Axcademy of Science
210
3
197-208
Yes (verified by ORBilu)
0039-3223
1730-6337
Warszawa
Poland
[en] Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of bounded linear operators on H with the weak operator topology. We prove that if U is a measurable map from G to L(H) then it is continuous. This result was known before for separable H. We also prove that the following statement is consistent with ZFC: every measurable homomorphism from a locally compact group into any topological group is continuous.
http://hdl.handle.net/10993/26362
10.4064/sm210-3-1

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