At. Lau et al., LOCALLY COMPACT-GROUPS, INVARIANT-MEANS AND THE CENTERS OF COMPACTIFICATIONS, Journal of the London Mathematical Society, 56, 1997, pp. 77-90
This paper brings together two apparently unrelated results about loca
lly compact groups G by giving them a common proof. The first concerns
the number of topologically left invariant means on L-infinity(G), wh
ile the second slates that the topological centre of the largest semig
roup compactification of G is simply G itself. On the way, we introduc
e as vital tools some new compactifications of the half line ([0, infi
nity), +), we produce a right invariant pseudometric on a compactly ge
nerated G for which the bounded sets are precisely the relatively comp
act sets, and we receive striking confirmation that some algebraic pro
perties of semigroups can be transferred by maps which are quite far f
rom being homomorphisms.