Derivations into duals of ideals of Banach algebras |
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Authors: | M. E. Gorgi T. Yazdanpanah |
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Affiliation: | (1) Department of Mathematics, Faculty of Sciences, Semnan University, Semnan, Iran;(2) Department of Mathematics, Teacher Training University, 599, Taleghani Avenue, 15614 Tehran, Iran |
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Abstract: | We introduce two notions of amenability for a Banach algebra A. LetI be a closed two-sided ideal inA, we sayA is I-weakly amenable if the first cohomology group ofA with coefficients in the dual space I* is zero; i.e.,H 1(A, I*) = {0}, and,A is ideally amenable ifA isI-weakly amenable for every closed two-sided idealI inA. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study theI-weak amenability of a Banach algebraA for some special closed two-sided idealI. |
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Keywords: | Amenability weak-amenability ideal weak-amenability |
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