Derivations on the module extension Banach algebras

UDC 517.986 We correct some results presented in [M. Eshaghi Gordji, F. Habibian, A. Rejali, <em> Ideal amenability of module extension Banach algebras</em>, Int. J. Contemp. Math. Sci., <strong>2</strong>, No. 5, 213–219 (2007)] and, using the obtained consequences, we find necessary and sufficient conditions for the module extension to be -weakly amenable, where is a closed ideal of the Banach algebra and is a closed -submodule of the Banach -bimodule We apply this result to the module extension where are two Banach -bimodules.

Derivations into annihilators of the ideals of Banach algebras

In this article, following Gorgi and Yazdanpanah, we define two new concepts of the ideal amenability for a Banach algebra A. We compare these notions with J-weak amenability and ideal amenability, where J is a closed two-sided ideal in A. We also study the hereditary properties of quotient ideal amenability for Banach algebras. Some examples show that the concepts of A/J-weak amenability and of J-weak amenability do not coincide for Banach algebras in general.

ON n-IDEAL AMENABILITY OF CERTAIN BANACH ALGEBRAS

In this paper we consider some notions of amenability such as ideal amenability, n-ideal amenability and approximate n-ideal amenability. The first two were introduced and studied by Gordji, Yazdanpanah and Memarbashi. We investigate some properties of certain Banach algebras in each of these classes. Results are also given for Segal algebras on locally compact groups.