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/