Geodesic
On continuity of measurable group representations and homomorphisms
Yulia Kuznetsova1
1 University of Franche-Comté 25030 Besançon Cedex, France and University of Luxembourg 6, rue Richard Coudenhove-Kalergi L-1359 Luxembourg
Studia Mathematica, Tome 210 (2012) no. 3, pp. 197-208

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $G$ be a locally compact group, and let $U$ be its unitary representation on a Hilbert space $H$. Endow the space $\mathcal L(H)$ of bounded linear operators on $H$ with the weak operator topology. We prove that if $U$ is a measurable map from $G$ to $\mathcal L(H)$ 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.
DOI : 10.4064/sm210-3-1
Keywords: locally compact group its unitary representation hilbert space endow space mathcal bounded linear operators weak operator topology prove measurable map mathcal continuous result known before separable prove following statement consistent zfc every measurable homomorphism locally compact group topological group continuous

Yulia Kuznetsova 1

1 University of Franche-Comté 25030 Besançon Cedex, France and University of Luxembourg 6, rue Richard Coudenhove-Kalergi L-1359 Luxembourg 
@article{10_4064_sm210_3_1,
     author = {Yulia Kuznetsova},
     title = {On continuity of measurable group representations and
homomorphisms},
     journal = {Studia Mathematica},
     pages = {197--208},
     publisher = {mathdoc},
     volume = {210},
     number = {3},
     year = {2012},
     doi = {10.4064/sm210-3-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm210-3-1/}
}
TY  - JOUR
AU  - Yulia Kuznetsova
TI  - On continuity of measurable group representations and
homomorphisms
JO  - Studia Mathematica
PY  - 2012
SP  - 197
EP  - 208
VL  - 210
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm210-3-1/
DO  - 10.4064/sm210-3-1
LA  - en
ID  - 10_4064_sm210_3_1
ER  - 
%0 Journal Article
%A Yulia Kuznetsova
%T On continuity of measurable group representations and
homomorphisms
%J Studia Mathematica
%D 2012
%P 197-208
%V 210
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm210-3-1/
%R 10.4064/sm210-3-1
%G en
%F 10_4064_sm210_3_1
Yulia Kuznetsova. On continuity of measurable group representations and
homomorphisms. Studia Mathematica, Tome 210 (2012) no. 3, pp. 197-208. doi: 10.4064/sm210-3-1

Cité par Sources :