On character amenability of restricted semigroup algebras

다국어 초록 (Multilingual Abstract)

We study the character amenability of restricted semigroup algebra ℓ¹r(S) and that of the semigroup algebra ℓ¹(Sr) on restricted semigroup Sr. We work on certain semigroups such as restricted semigroups, Clifford semigroups, Brandt semigroups and semilattice. In particular, we show that for a Clifford semigroup S, the character amenability of ℓ¹(Sr) is equivalent to that of ℓ¹r (S), this is in turn equivalent to ℓ¹(S) being an amenable Banach algebra. This same result was also shown to be true for a Brandt semigroup S over a group G with a finite index set J.

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