In the first part of the paper, some criteria of continuity of representations of a Polish group in a Banach algebra are given. The second part uses the result of the first part to deduce automatic continuity results of Baire morphisms from Polish groups to locally compact groups or unitary groups. In the final part, the spectrum of an element in the range of a strongly but not norm continuous representation is described.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-1-3,
author = {M. Cianfarani and J.-M. Paoli and P. Simonnet and J.-C. Tomasi},
title = {Representations of Polish groups and continuity},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {27-52},
zbl = {1336.22005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-1-3}
}
M. Cianfarani; J.-M. Paoli; P. Simonnet; J.-C. Tomasi. Representations of Polish groups and continuity. Studia Mathematica, Tome 223 (2014) pp. 27-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-1-3/