let s be a semigroup. in certain cases we give some characterizations of extreme amenability of s and we show that in these cases extreme left amenability and extreme right amenability of s are equivalent. also when s is a compact topological semigroup, we characterize extremely left amenable subalgebras of c(s), where c(s) is the space of all continuous bounded real valued functions on s

The concept of amenability for Banach algebras was introduced by Johnson in 1972 [6]. Several modifications of this notion, such as approximate amenability and pseudo-amenability, were introduced in [2] and [4]. In the current paper we investigate the pseudo-amenability of Brandt semigroup algebras. It was shown in [2] and [4] that for the group algebra L(G), amenability, approximate amenabilit...

There are two notions of amenability for discrete equivalence relations. The \global" amenability (which is usually referred to just as \amenability") is the property of existence of leafwise invariant means, which, by a theorem of Connes{Feldman{Weiss, is equivalent to hyperrniteness, or, to being the orbit equivalence relation of a Z-action. The notion of \local" amenability applies to equiva...

We prove that the following are equivalent for a locally compact group G: (i) G is amenable; (ii) M(G) is Connes-amenable; (iii) M(G) has a normal, virtual diagonal.