Abstract
For a large class of locally compact semitopological semigroups S, the Stone-Cech compactification βS is a semigroup compactification if and only if S is either discrete or countably compact. Furthermore, for this class of semigroups which are neither discrete nor countably compact, the quotient \(\ensuremath {\mathcal {C}_{b}}(S)/\ensuremath {\mathcal {LMC}}(S)\) contains a linear isometric copy of l∞. These results improve theorems by Baker and Butcher and by Dzinotyiweyi.
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