[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.
Disciplines :
Mathématiques
Auteur, co-auteur :
KUZNETSOVA, Julia ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Co-auteurs externes :
no
Langue du document :
Anglais
Titre :
On continuity of measurable group representations and homomorphisms
