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The generalized notion of weak amenability, namely -weak amenability, where are continuous homomorphisms on a Banach algebra , was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the -weak amenability on the measure algebra , the group algebra and the Segal algebra , where is a locally compact group, are studied. As a typical example, the -weak amenability of a special semigroup algebra is shown as well.
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