The Characterizations of Extreme Amenability of Locally Compact Semigroups

Abstract EN

We demonstrate that the characterizations of topological extreme amenability.

In particular, we prove that for every locally compact semigroup S with a right identity, the condition μ⊙(F×G)=(μ⊙F)×(μ⊙G), for F, G in M(S)∗, and 0<μ∈M(S), implies that μ=εa, for some a∈S (εa is a Dirac measure).

We also obtain the conditions for which M(S)∗ is topologically extremely left amenable.