Let A be a Banach algebra and I closed ideal of A. We say that is amenable relative to I, if A/I an algebra. study the amenability algebras investigate triangular associated locally compact groups. generalize some previous known results by applying concept algebras, especially, we present generalization Johnson?s theorem in amenability.

We use random walks to show that the Basilica group is amenable, answering an open question of Grigorchuk and Żuk. Our results separate the class of amenable groups from the closure of subexponentially growing groups under the operations of group extension and direct limits; these classes are separated even within the realm of finitely presented groups.

Abstract We describe how properties of metric groups and unitary representations can be presented in continuous logic. In particular we find L ω 1 -axiomatization amenability. also show that the case locally compact some uniform version negation Kazhdan’s property (T) viewed as a union first-order axiomatizable classes. will see when these are preserved under taking elementary substructures.

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...