Approximate Amenability of Certain Semigroup Algebras |
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Authors: | M. Lashkarizadeh Bami H. Samea |
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Affiliation: | (1) Department of Mathematics, Isfahan University, Isfahan, Iran |
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Abstract: | In the present paper, it is shown that a left cancellative semigroup S (not necessarily with identity) is left amenable whenever the Banach algebra ℓ1(S) is approximately amenable. It is also proved that if S is a Brandt semigroup over a group G with an index set I, then ℓ1(S) is approximately amenable if and only if G is amenable. Moreover ℓ1(S) is amenable if and only if G is amenable and I is finite. For a left cancellative foundation semigroup S with an identity such that for every Ma(S)-measurable subset B of S and s ∈ S the set sB is Ma(S)-measurable, it is proved that if the measure algebra Ma(S) is approximately amenable, then S is left amenable. Concrete examples are given to show that the converse is negative. |
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