EUDML

Currently displaying 1 – 11 of 11

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Markov operators on the solvable Baumslag-Solitar groups.

Martin, Florian; Valette, Alain — 2000

Experimental Mathematics

Idempotents in complex group rings: Theorems of Zalesskij and Bass revisited.

Burger, Marc; Valette, Alain — 1998

Journal of Lie Theory

Nouvelles approches de la propriété (T) de Kazhdan

Alain Valette

Séminaire Bourbaki

Un groupe localement compact $G$ a la propriété (T) de Kazhdan si la $1$ -cohomologie de tout $G$ -module hilbertien est nulle. Cette propriété de rigidité de la théorie des représentations de $G$ a trouvé des applications qui vont de la théorie ergodique à la théorie des graphes. Pendant près de 30 ans, les seuls exemples connus de groupes avec la propriété (T), provenaient des groupes algébriques simples sur les corps locaux, ou de leurs réseaux. La situation a radicalement changé ces dernières années :...

Graphes de Ramanujan et applications

Alain Valette

Séminaire Bourbaki

An application of Ramanujan graphs to C*-algebra tensor products, II

Alain Valette

Séminaire de théorie spectrale et géométrie

Projections in full C*-algebras of semisimple Lie groups.

Alain Valette — 1992

Mathematische Annalen

On the Haagerup inequality and groups acting on ${\tilde{A}}_{n}$ -buildings

Alain Valette — 1997

Annales de l'institut Fourier

Let $Γ$ be a group endowed with a length function $L$ , and let $E$ be a linear subspace of $C Γ$ . We say that if there exists constants $C, s > 0$ such that, for any $f \in E$ , the convolutor norm of $f$ on $ℓ^{2} (Γ)$ is dominated by $C$ times the $ℓ^{2}$ norm of $f (1 + L)^{s}$ . We show that, for $E = C Γ$ , the Haagerup inequality can be expressed in terms of decay of random walks associated with finitely supported symmetric probability measures on $Γ$ . If $L$ is a word length function on a finitely generated group $Γ$ , we show that, if the space ${Rad}_{L} (Γ)$ of radial functions...

Kazhdan's property (T) and amenable representations.

Alain Valette; M.E.B. Bekka — 1993

Mathematische Zeitschrift

On $1$ -cocycles induced by a positive definite function on a locally compact abelian group

Jordan Franks; Alain Valette — 2014

Annales mathématiques Blaise Pascal

For $ϕ$ a normalized positive definite function on a locally compact abelian group $G$ , let $π_{ϕ}$ be the unitary representation associated to $ϕ$ by the GNS construction. We give necessary and sufficient conditions for the vanishing of 1-cohomology $H^{1} (G, π_{ϕ})$ and reduced 1-cohomology ${\bar{H}}^{1} (G, π_{ϕ})$ . For example, ${\bar{H}}^{1} (G, π_{ϕ}) = 0$ if and only if either $Hom (G, ℂ) = 0$ or $μ_{ϕ} (1_{G}) = 0$ , where $1_{G}$ is the trivial character of $G$ and $μ_{ϕ}$ is the probability measure on the Pontryagin dual $\hat{G}$ associated to $ϕ$ by Bochner’s Theorem. This streamlines an argument of Guichardet (see Theorem...