Exposés à venir

-Mardi 13 septembre: Marek Cúth, Université Charles, Prague.
Embedding of ℓ1 into Lipschitz-free Banach spaces and ℓ∞ into their duals

Given a metric space M, it is possible to construct a Banach space ℱ(M) in such a way that the Lipschitz structure of M corresponds to the linear structure of ℱ(M). This space ℱ(M) is sometimes called the "Lipschitz-free space over M". The study of Lipschitz-free Banach spaces became an active field of study. I will present our recent result with M. Johanis that ℓ∞ embeds isometrically into the dual of every infinite-dimensional Lipschitz-free Banach space and that it is often the case that a Lipschitz-free Banach space contains a 1-complemented subspace isometric to ℓ1. We do not know whether the later is true for every infinite-dimensional Lipschitz-free Banach space.

-Mardi 20 septembre: Safoura Jafar-Zadeh , UFC.
Isometric isomorphisms of the annihilator of $C_0(G)$ in $LUC(G)^*$

For a locally compact group $G$, let $C_b(G)$ be the space of all complex-valued, continuous and bounded functions on $G$ equipped with the sup-norm, and $LUC(G)$ be the subspace of $C_b(G)$ consisting of all functions $f$ such that the map $G\to C_b(G);x\mapsto l_xf$ is continuous, where $l_xf$ is the function defined by $l_xf(y)=f(xy)$, for each $y\in G.$ In this talk, I will show that if $G$ is a locally compact group and $H$ is a discrete group then whenever there exists a weak-star continuous isometric isomorphism between $C_0(G)^\perp$ (the annihilator of $C_0(G)$ in $LUC(G)^*$) and $C_0(H)^\perp$, then $G$ is isomorphic to $H$ as a topological group. Several related results will also be discussed.

-Mardi 27 septembre: Uwe Franz, UFC.
HUNT FORMULA FOR SUq(n) AND Uq(n)

Joint work with Anna Kula, Martin Lindsay, and Michael Skeide. We provide a Hunt type formula for the infinitesimal generators of Lévy process on the compact quantum groups SUq(N )and Uq(N ). In particular, we obtain a decomposition of such generators into a gaussian part and a "jump" type part, similar to the classical Hunt formula.