We introduce a bounded version of Bredon cohomology for groups relative to family subgroups. Our theory generalizes and differs from Mineyev--Yaman's pairs. obtain cohomological characterizations amenability hyperbolicity, analogous the results Johnson Mineyev cohomology.

In this paper, we give a short survey of results and problems concerning the notion of bounded weak approximate identities in Banach algebras. Also, we introduce a new version of approximate identities and give one illuminating example to show the difference.

We derive simple explicit formula for the character of a cycle in the Connes’ (b, B)-bicomplex of cyclic cohomology and apply it to write formulas for the equivariant Chern character and characters of finitely-summable bounded Fredholm modules.

Introduction The coarse Baum-Connes conjecture states that a certain coarse assembly map µ : KX * (X) → K * (C * (X)) is an isomorphism (see for example [Roe96] or the piece by N. Higson and J. Roe in [FRR95]). It has many important consequences including one of the main motivations for this piece: a descent technique connects it to injectivity of the ('ordinary') Baum-Connes assembly map µ : K...

Let G be a locally compact group. We use the canonical operator space structure on the spaces L(G) for p ∈ [1,∞] introduced by G. Pisier to define operator space analoguesOAp(G) of the classical Figà-Talamanca–Herz algebrasAp(G). If p ∈ (1,∞) is arbitrary, then Ap(G) ⊂ OAp(G) such that the inclusion is a contraction; if p = 2, then OA2(G) ∼= A(G) as Banach spaces spaces, but not necessarily as ...