On continuity of measurable group representations and
homomorphisms
Studia Mathematica, Tome 210 (2012) no. 3, pp. 197-208
Cet article a éte moissonné depuis 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.
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
Affiliations des auteurs :
Yulia Kuznetsova 1
@article{10_4064_sm210_3_1,
author = {Yulia Kuznetsova},
title = {On continuity of measurable group representations and
homomorphisms},
journal = {Studia Mathematica},
pages = {197--208},
year = {2012},
volume = {210},
number = {3},
doi = {10.4064/sm210-3-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/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
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