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...

Let A be a Banach algebra and X a Banach A-bimodule, the derivation D : A → X is semi-inner if there are ξ, μ ∈ X such that D(a) = a.ξ − μ.a, (a ∈ A). A is called semi-amenable if every derivation D : A → X∗ is semi-inner. The dual Banach algebra A is Connes semi-amenable (resp. approximately semi-amenable) if, every D ∈ Z1w _ (A,X), for each normal, dual Banach A-bimodule X, is semi -inner (re...

This paper summarizes various interpretations of emotional arguments, with a focus on the mode argument introduced in multi-modal argumentation model (Gilbert, 1994). From there author shifts from descriptive account arguments to discussion about normative framework. Pointing out problems evaluative models mode, paradigmatic shift captured by Amenable Argumentation Approach is explained as way ...

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.