On continuity of measurable group representations and homomorphisms

Yulia Kuznetsova. "On continuity of measurable group representations and homomorphisms." Studia Mathematica 210.3 (2012): 197-208. <http://eudml.org/doc/285588>.

@article{YuliaKuznetsova2012,
abstract = {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.},
author = {Yulia Kuznetsova},
journal = {Studia Mathematica},
keywords = {automatic continuity; Polish groups; group representations; homomorphisms of groups; non-measurable unions; unions of null sets; consistency of ZFC axioms and set theory},
language = {eng},
number = {3},
pages = {197-208},
title = {On continuity of measurable group representations and homomorphisms},
url = {http://eudml.org/doc/285588},
volume = {210},
year = {2012},
}

TY - JOUR
AU - Yulia Kuznetsova
TI - On continuity of measurable group representations and homomorphisms
JO - Studia Mathematica
PY - 2012
VL - 210
IS - 3
SP - 197
EP - 208
AB - 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.
LA - eng
KW - automatic continuity; Polish groups; group representations; homomorphisms of groups; non-measurable unions; unions of null sets; consistency of ZFC axioms and set theory
UR - http://eudml.org/doc/285588
ER -