in this paper we study the concept of ph-biatness ofa banach algebra a, where ph is a continuous homomorphism on a.we prove that if ph is a continuous epimorphism on a and a hasa bounded approximate identity and a is ph- biat, then a is ph-amenable. in the case where ph is an isomorphism on a we showthat the ph- amenability of a implies its ph-biatness.

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

We show how the Connes–Moscovici bialgebroid construction naturally provides universal objects for Lie algebras acting on non-commutative algebras. As a supplement, we see these interact with study of flat bimodule connections.

We give an account of the Connes-Kreimer renormalization in the context of connected graded Hopf algebras. We first explain the Birkhoff decomposition of characters in the more general context of connected filtered Hopf algebras, then specializing down to the graded case in order to introduce the notions of locality, renormalization group and Connes-Kreimer’s Beta function. The connection with ...

We construct for an equivariant homology theory for proper equivariant CW -complexes an equivariant Chern character under certain conditions. This applies for instance to the sources of the assembly maps in the Farrell-Jones Conjecture with respect to the family F of finite subgroups and in the Baum-Connes Conjecture. Thus we get an explicit calculation of Q ⊗Z Kn(RG) and Q ⊗Z Ln(RG) for a comm...

The central result of this paper is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby gener...

An extension of the Connes–Lott model is proposed. It is also within the framework of the A.Connes construction based on a generalized Dirac–Yukawa operator and the K–cycle (H,D), with H a fermionic Hilbert space. The basic algebra A which may be considered as representing the non–commutative extension, plays a less important role in our approach. This allows a new class of natural extensions. ...

We show that Connes’ embedding conjecture on von Neumann algebras is equivalent to the existence of certain algebraic certificates for a polynomial in noncommuting variables to satisfy the following nonnegativity condition: The trace is nonnegative whenever self-adjoint contraction matrices of the same size are substituted for the variables. These algebraic certificates involve sums of hermitia...

A topological group G is extremely amenable if every continuous action of G on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of a Lebesgue space with a non-atomic measure is extremely amenable with the weak topology but not with the uniform one. Strengthening a de la Harpe’s result, we sh...

It is known that B(l) is not amenable for p = 1, 2,∞, but whether or not B(l) is amenable for p ∈ (1,∞) \ {2} is an open problem. We show that, if B(l) is amenable for p ∈ (1,∞), then so are l(B(l)) and l(K(l)). Moreover, if l(K(l)) is amenable so is l(I,K(E)) for any index set I and for any infinite-dimensional Lspace E; in particular, if l(K(l)) is amenable for p ∈ (1,∞), then so is l(K(l ⊕ l...