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DERIVATIONS INTO N-TH DUALS OF IDEALS OF BANACH ALGEBRAS Communicated by Fereidoun Ghahramani

2008
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Bulletin of the Iranian Mathematical Society
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unpublished

We introduce two notions of amenability for a Banach algebra A. Let n ∈ N and I be a closed two-sided ideal in A. A is n − I−weakly amenable if the first cohomology group of A with coefficients in the n-th dual space I (n) is zero; i.e., H 1 (A, I (n)) = {0}. Further, A is n-ideally amenable if A is n−I−weakly amenable for every closed two-sided ideal I in A. We find some relationships of n − I− weak and m − J− weak amenabilities for some different m and n or for different closed ideals I and J of A.

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