International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 207016, 18 pages
doi:10.1155/2008/207016
Research Article
The Characterizations of Extreme Amenability of Locally Compact Semigroups
Department of Mathematics, Faculty of Science, K. N. Toosi University of Technology, P.O. Box 16315 - 1618, Tehran 19697, Iran
Received 15 May 2008; Revised 22 August 2008; Accepted 10 November 2008
Academic Editor: Michael Tom
Copyright © 2008 Hashem Masiha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.