On va étudier le comportement asymptotique d’une intégrale de type intégrale de Itzykson-Zuber et on va donner une formule pour sa limite. On va obtenir ce résultat en utilisant un théorème de Poincaré et un théorème de Minlos.

If the Poisson integral of the unit disc is replaced by its square root, it is known that normalized Poisson integrals of $L^p$ and weak $L^p$ boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning and the author, respectively. In this paper we characterize the approach regions for boundary functions in two general classes of Orlicz spaces. The first of these classes contains spaces $L^{\Phi }$ having the property $L^{\infty }\subset L^{\Phi }\subset L^p$, $1\le p<\infty$. The second contains spaces $L^{\Phi }$ that...

We consider when certain Banach sequence algebras A on the set ℕ are approximately amenable. Some general results are obtained, and we resolve the special cases where $A={\ell }^p$ for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras ${\ell }^p\left(\omega \right)$.

The notions of approximate amenability and weak amenability in Banach algebras are formally stronger than that of approximate weak amenability. We demonstrate an example confirming that approximate weak amenability is indeed actually weaker than either approximate or weak amenability themselves. As a consequence, we examine the (failure of) approximate amenability for ${\ell }^p$-sums of finite-dimensional normed algebras.

We study the relationship between the classical invariance properties of amenable locally compact groups G and the approximate diagonals possessed by their associated group algebras L¹(G). From the existence of a weak form of approximate diagonal for L¹(G) we provide a direct proof that G is amenable. Conversely, we give a formula for constructing a strong form of approximate diagonal for any amenable locally compact group. In particular we have a new proof of Johnson's Theorem: A locally compact...

We continue our study of derivations, multipliers, weak amenability and Arens regularity of Segal algebras on locally compact groups. We also answer two questions on Arens regularity of the Lebesgue-Fourier algebra left open in our earlier work.

Soient $G_1$ et $G_2$ deux groupes abéliens localement compacts de dual ${\Gamma }_1$ et ${\Gamma }_2$. Soit $h:{\Gamma }_1\to {\Gamma }_2$ un homomorphisme continu d’image dense de ${\Gamma }_1$ dans ${\Gamma }_2$. Soit $1\le p\le \infty$ ; on prouve un théorème d’approximation des multiplicateurs de $\mathbf{F}{L}^p(G_2)$ et on utilise ce résultat pour démontrer le suivant : soit $m:{\Gamma }_2\to \mathbf{C}$ une fonction continue ; $m$ est un multiplicateur de $\mathbf{F}{L}^p(G_2)$ si, et seulement si, $m\circ h$ est un multiplicateur de $\mathbf{F}{L}^p(G_1)$.

We study the Arens regularity of module actions of Banach left or right modules over Banach algebras. We prove that if has a brai (blai), then the right (left) module action of on * is Arens regular if and only if is reflexive. We find that Arens regularity is implied by the factorization of * or ** when is a left or a right ideal in **. The Arens regularity and strong irregularity of are related to those of the module actions of on the nth dual ${}^{\left(n\right)}$ of . Banach algebras for which Z( **) = but $⊊Z^t(**)$ are...