Let $G$ be a locally compact abelian group and $C{V}_p\left(G\right)$$(1\le p\le 2)$ be the space of bounded convolution...

We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.

A semigroup $H$ in ${\mathbf{L}}_s\left(E\right)$, $E$ a Banach space, is called mean ergodic, if its closed convex hull in ${\mathbf{L}}_s\left(E\right)$ has a zero element. Compact groups, compact abelian semigroups or contractive semigroups on Hilbert spaces are mean ergodic.Banach lattices prove to be a natural frame for further mean ergodic theorems: let $H$ be a bounded semigroup of positive operators on a Banach lattice $E$ with order continuous norm. $H$ is mean ergodic if there is a $H$-subinvariant quasi-interior point of $E_{+}$ and a $H^{\text{'}}$-subinvariant strictly...

Let $S$ be an inverse semigroup with the set of idempotents $E$ and $S/\approx$ be an appropriate group homomorphic image of $S$. In this paper we find a one-to-one correspondence between two cohomology groups of the group algebra ${\ell }^1\left(S\right)$ and the semigroup algebra ${\ell }^1(S/\approx )$ with coefficients in the same space. As a consequence, we prove that $S$ is amenable if and only if $S/\approx$ is amenable. This could be considered as the same result of Duncan and Namioka [5] with another method which asserts that the inverse semigroup $S$ is amenable...

In 2005, the paper [KPT05] by Kechris, Pestov and Todorcevic provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow. This immediately led to an explicit representation of this invariant in many concrete cases. However, in some particular situations, the framework of [KPT05] does not allow one to perform the computation directly, but only after a slight modification of the original argument. The purpose of the present paper is to supplement [KPT05]...

On présente des conditions suffisantes pour qu’une extension HNN soit intérieurement moyennable, respectivement CCI, qui donnent des critères nécessaires et suffisants parmi les groupes de Baumslag-Solitar. On en déduit qu’un tel groupe, vu comme groupe d’automorphismes de son arbre de Bass-Serre, possède des éléments non triviaux qui fixent des sous-arbres non bornés.

Il est bien connu qu’une fonction $f$ sur ${ℝ}^n$ est harmonique - Δf = 0 - si et seulement si sa moyenne sur toute sphère est égale à sa valeur au centre de cette sphère. De manière semblable, f vérifie l’équation de Helmholtz Δf + cf = 0 si et seulement si sa moyenne sur la sphère de centre x et de rayon r vaut $\Gamma (n/2){(r\surd c/2)}^{(2-n)/2}{J}_{(n-2)/2}\left(r\surd c\right)·f\left(x\right)$. Dans ce travail, nous généralisons ces résultats à l’opérateur ${(\Delta +c)}^k$ où k est un entier strictement positif et c une constante non nulle. Bien qu’une méthode pour y parvenir soit esquissée dans...