Ideal amenability of Banach algebras on locally compact groups |
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Authors: | M Eshaghi Gordji S A R Hosseiniun |
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Institution: | (1) Department of Mathematics, Faculty of Sciences, Semnan University, Semnan, Iran;(2) Department of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran |
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Abstract: | In this paper we study the ideal amenability of Banach algebras. LetA be a Banach algebra and letI be a closed two-sided ideal inA, A isI-weakly amenable ifH
1(A,I
*) = {0}. Further,A is ideally amenable ifA isI-weakly amenable for every closed two-sided idealI inA. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability
the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal
amenability of Banach algebras on locally compact groups. |
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Keywords: | Amenability derivation ideally amenable weak amenability |
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