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On character amenability of restricted semigroup algebras

O. T. Mewomo|O.J. Ogunsola
장전수학회 (Jangjeon Mathematical Society)|2016.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제19권 제3호|pp. 591-607|DOI 10.17777/pjms.2016.19.3.014

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키워드

Banach algebraSemigroupSemigroup algebrarestricted semigrouprestricted semigroup alge- bracharacter amenable
주제분류수학

초록

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.

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.

참고문헌 (28)

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