2005/03/05 by M E Gorgi, T Yazdanpanah
Mathematics · #math.FA
published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 4, November 2004, pp. 399-408 · 10 pages
arxiv created 2005/03/05 · arxiv updated 2009/12/01
We introduce two notions of amenability for a Banach algebra \cal A. Let I be a closed two-sided ideal in \cal A, we say \cal A is I-weakly amenable if the first cohomology group of \cal A with coefficients in the dual space I^* is zero; i.e., H1(\cal A,I^*)=\0\, and, \cal A is ideally amenable if \cal A is I-weakly amenable for every closed two-sided ideal I in \cal A. 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 the I-weak amenability of a Banach algebra \cal A for some special closed two-sided\break ideal I.