Let A be an A*-algebra with enveloping C*-algebra C*(A). We show that, under certain conditions, a homomorphism from C*(A) into a Banach algebra is continuous if and only if its restriction to A is continuous. We apply this result to the question in the title.
@article{bwmeta1.element.bwnjournal-article-smv110i1p97bwm,
author = {Volker Runde},
title = {When is there a discontinuous homomorphism from L$^1$(G)?},
journal = {Studia Mathematica},
volume = {108},
year = {1994},
pages = {97-104},
zbl = {0829.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv110i1p97bwm}
}
Runde, Volker. When is there a discontinuous homomorphism from L¹(G)?. Studia Mathematica, Tome 108 (1994) pp. 97-104. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv110i1p97bwm/
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