In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

let  and  be banach algebras, ,  and . we define an -product on  which is a strongly splitting extension of  by . we show that these products form a large class of banach algebras which contains all module extensions and triangular banach algebras. then we consider spectrum, arens regularity, amenability and weak amenability of these products.

Over a field of characteristic zero, we introduce two motivic operations on additive higher Chow cycles: analogues of the Connes boundary B operator and the shuffle product on Hochschild complexes. The former allows us to apply the formalism of mixed complexes to additive Chow complexes building a bridge between additive higher Chow theory and additive K-theory. The latter induces a wedge produ...

Nous cherchons à comprendre pourquoi la propriété (T) de Kazhdan [Kaz67, HV89, BHV08], et plus particulièrement une forme renforcée de celle-ci introduite dans [Laf08], sont un obstacle à une démonstration de la surjectivité de l’application de Baum-Connes à coefficients arbitraires pour des groupes ayant un élément γ de Kasparov, à l’aide des méthodes connues. Nous passons d’abord en revue tro...

We introduce the concept of para-Hopf algebroid and define their cyclic cohomology in the spirit of Connes-Moscovici cyclic cohomology for Hopf algebras. Para-Hopf algebroids are closely related to, but different from, Hopf algebroids. Their definition is motivated by attempting to define a cyclic cohomology theory for Hopf algebroids in general. We show that many of Hopf algebraic structures, ...

In [3], Connes found a conformal invariant using Wodzicki’s 1-density and computed it in the case of 4-dimensional manifold without boundary. In [14], Ugalde generalized the Connes’ result to n-dimensional manifold without boundary. In this paper, we generalize the results of [3] and [14] to the case of manifolds with boundary. Subj. Class.: Noncommutative global analysis; Noncommutative differ...

In this paper we consider a family of Dirac-type operators on fibration P → B equivariant with respect to an action of an étale groupoid. Such a family defines an element in the bivariant K theory. We compute the action of the bivariant Chern character of this element on the image of Connes’ map Φ in the cyclic cohomology. A particular case of this result is Connes’ index theorem for étale grou...