in this paper we investigate some hereditary properties of amenability modulo an ideal of banach algebras. we show that if (e) is a bounded approximate identity modulo i of a banach algebra a and x is a neo-unital modulo i, then (e) is a bounded approximate identity for x. moreover we show that amenability modulo an ideal of a banach algebra a can be only considered by the neo-unital modulo...

We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R. J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtain...

In this paper, we introduce a concept of an evacuation scheme on the Cayley graph infinite finitely generated group. This is collection simple paths bringing all vertices to infinity. We impose restriction that every edge can be used uniformly bounded number times in scheme. An easy observation shows existence such equivalent non-amenability A special case happens if only once. These schemes ar...