Produit croisé d'une algèbre de Kac par un groupe localement compact
Produits finis de commutateurs dans les -algèbres
Soient une -algèbre approximativement finie simple avec unité, le groupe des inversibles et le groupe des unitaires de . Nous avons défini dans un précédent travail un homomorphisme , appelé déterminant universel de , de sur un groupe abélien associé à . Nous montrons ici que, pour qu’un élément dans ou dans soit produit d’un nombre fini de commutateurs, il (faut et il) suffit que Ceci permet en particulier d’identifier le noyau de la projection canonique On établit aussi...
Progrès récents sur la conjecture de Baum-Connes. Contribution de Vincent Lafforgue
Projections from a von Neumann algebra onto a subalgebra
Projections in C*-Algebras of nilpotent groups.
Projections in full C*-algebras of semisimple Lie groups.
Projective C*-algebras.
Projective tensor products of C*-algebras.
Projectively invariant Hilbert-Schmidt kernels and convolution type operators
We consider positive definite kernels which are invariant under a multiplier and an action of a semigroup with involution, and construct the associated projective isometric representation on a Hilbert C*-module. We introduce the notion of C*-valued Hilbert-Schmidt kernels associated with two sequences and construct the corresponding reproducing Hilbert C*-module. We also discuss projective invariance of Hilbert-Schmidt kernels. We prove that the range of a convolution type operator associated with...
Property T for discrete groups in terms of their regular representation.
Property (T) for ... Factors and unitary representations of Kazhdan groups.
Pseudometrics on Ext-semigroups
This paper considers certain pseudometric structures on Ext-semigroups and gives a unified characterization of several topologies on Ext-semigroups. It is demonstrated that these Ext-semigroups are complete topological semigroups. To this end, it is proved that a metric induces a pseudometric on a quotient space with respect to an equivalence relation if it has certain invariance. We give some properties of this pseudometric space and prove that the topology induced by the pseudometric coincides...
Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations
For any pair E,F of pseudotopological vector spaces, we endow the space L(E,F) of all continuous linear operators from E into F with a pseudotopology such that, if G is a pseudotopological space, then the mapping L(E,F) × L(F,G) ∋ (f,g) → gf ∈ L(E,G) is continuous. We use this pseudotopology to establish a result about differentiability of certain operator-valued functions related with strongly continuous one-parameter semigroups in Banach spaces, to characterize von Neumann algebras, and to establish...
Pure Jauch-Piron states on von Neumann algebras
Pure States and P-Commutative Banach *-Algebras.
Pure states on Jordan algebras
We prove that a pure state on a -algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application we contribute...
Purely infinite -algebras arising from dynamical systems
Purely infinite C*-algebras from boundary actions of discrete groups.