In this paper, we will define and study amenability of Hopf C-algebras as well as that of Fourier duality. 1991 AMS Mathematics Classification number: 46L55, 46L05

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

in this paper we initiate the study of real group algebras and investigate some of its aspects.let l1 (g) be a group algebra of a locally compact group g,τ :g →g be a group homeomorphismsuch that τ 2 =τοτ = 1, the identity map, and lp (g,τ ) = { f ∈ lp (g) : fοτ = f } ( p ≥ 1) . in thispaper, among other results, we clarify the structure of lp (g,τ ) and characterize amenability ofl1 (g,τ ) and...

In a recent paper by H.X. Cao, J.H. Zhang and Z.B. Xu a α-Lipschitz operator from a compact metric space into a Banach space A is defined and characterized in a natural way in the sence that F : K → A is a α-Lipschitz operator if and only if for each σ ∈ X∗ the mapping σoF is a α-Lipschitz function. The Lipschitz operators algebras L(K,A) and l(K,A) are developed here further, and we study thei...

We extend the concept of amenability of a Banach algebra A to the case that there is an extra A -module structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A = l(S) as a Banach module over A= l(E) is module amenable iff S is amenable. When S is a discrete group, l(E) = C and this is just the celebrated Johnson’s theorem.

We formulate two new criteria of amenability of discrete equivalence relations: in terms of asymptotically invariant families of leafwise probability measures and in terms of isoperimetric properties of leafwise graph structures. These criteria lead to a geometric proof of the Connes{Feldman{Weiss theorem on coincidence of amenability and hyperrniteness for equivalence relations. Nous consid er...

Let G be a locally compact abelian group, and let p 2 1; 1). We show that the Segal algebra S p (G) is always weakly amenable, but that it is amenable only if G is discrete.

We introduce notions of finite presentation and co-exactness which serve as qualitative quantitative analogues finite-dimensionality for operator modules over completely contractive Banach algebras. With these we begin the development a local theory by introducing lifting property, nuclearity, semi-discreteness. For large class prove that property is equivalent to flatness, generalizing space r...