The Characterizations of Extreme Amenability of Locally Compact Semigroups

Hashem Masiha

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-18

Abstract:

We demonstrate that the characterizations of topological extreme amenability. In particular, we prove that for every locally compact semigroup 𠑆 with a right identity, the condition 𠜇 ⊙ ( ð ¹ Ã— ð º ) = ( 𠜇 ⊙ ð ¹ ) × ( 𠜇 ⊙ ð º ) , for ð ¹ , ð º in ð ‘€ ( 𠑆 ) ∗ , and 0 < 𠜇 ∈ ð ‘€ ( 𠑆 ) , implies that 𠜇 = 𠜀 ð ‘Ž , for some ð ‘Ž ∈ 𠑆 ( 𠜀 ð ‘Ž is a Dirac measure). We also obtain the conditions for which ð ‘€ ( 𠑆 ) ∗ is topologically extremely left amenable.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:207016

DOI: 10.1155/2008/207016

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