A generalization of the -weak amenability of Banach algebras.
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Let be an inverse semigroup with the set of idempotents and be an appropriate group homomorphic image of . In this paper we find a one-to-one correspondence between two cohomology groups of the group algebra and the semigroup algebra with coefficients in the same space. As a consequence, we prove that is amenable if and only if is amenable. This could be considered as the same result of Duncan and Namioka [5] with another method which asserts that the inverse semigroup...
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