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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-3-1,
author = {Yulia Kuznetsova},
title = {On continuity of measurable group representations and homomorphisms},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {197-208},
zbl = {1290.22002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-3-1}
}
Yulia Kuznetsova. On continuity of measurable group representations and homomorphisms. Studia Mathematica, Tome 209 (2012) pp. 197-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-3-1/