Let G be a locally compact, non-compact group and f a function defined on G; we prove that, if f is uniformly continuous with respect to the left (right) structure on G and with a power integrable with respect to the left (right) Haar measure on G, then f must vanish at infinity. We prove that left and right cannot be mixed.
@article{urn:eudml:doc:40239,
title = {Left and right on locally compact groups.},
journal = {Collectanea Mathematica},
volume = {47},
year = {1996},
pages = {179-186},
zbl = {0854.22004},
mrnumber = {MR1402068},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40239}
}
Carcano, Giovanna. Left and right on locally compact groups.. Collectanea Mathematica, Tome 47 (1996) pp. 179-186. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40239/