Nous introduisons un calcul fonctionnel pour les fonctions harmoniques sur un ouvert du plan complexe et à valeurs dans une algèbre de Banach à involution continue. Ensuite, nous donnons dans les algèbres hermitiennes deux extensions des théorèmes de von Neumann et de Ky Fan sur les contractions. Nous obtenons également les analogues du lemme de Schwarz et du théorème de Pick.
We consider the full group [φ] and topological full group [[φ]] of a Cantor minimal system (X,φ). We prove that the commutator subgroups D([φ]) and D([[φ]]) are simple and show that the groups D([φ]) and D([[φ]]) completely determine the class of orbit equivalence and flip conjugacy of φ, respectively. These results improve the classification found in [GPS]. As a corollary of the technique used, we establish the fact that φ can be written as a product of three involutions from [φ].
We continue our study of topological partial *-algebras, focusing our attention on *-semisimple partial *-algebras, that is, those that possess a multiplication core and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals, and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the aim of characterizing a *-semisimple partial...
Let G be a compactly generated, locally compact group with polynomial growth and let ω be a weight on G. We look for general conditions on the weight which allow us to develop a functional calculus on a total part of L1(G,ω). This functional calculus is then used to study harmonic analysis properties of L1(G,ω), such as the Wiener property and Domar's theorem.