2005/08/25 by M Eshaghi Gordji, S A R Hosseiniun
Mathematics · #math.FA #msc:46H20
published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 3, August 2005, pp. 319-325 · 7 pages, no figures, no tables
arxiv created 2005/08/25 · arxiv updated 2009/12/01
In this paper we study the ideal amenability of Banach algebras. Let \cal A be a Banach algebra and let I be a closed two-sided ideal in \cal A, \cal A is I-weakly amenable if H1(\cal A,I^*)=\0\. Further, \cal A is ideally amenable if \cal A is I-weakly amenable for every closed two-sided ideal I in \cal A. 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.