Strong Ditkin algebras without bounded relative units.
Sur la continuité automatique des épimorphismes dans les -algèbres de Banach.
Sur le théorème de complétion de Buchwalter-Pupier
Sur les algèbres de Banach et les opérateurs -sommants
Sur les algèbres uniformes ayant mêmes parties réelles que certaines algèbres
Dans quelle mesure une algèbre uniforme est-elle déterminée par l’espace vectoriel des parties réelles de ses éléments ? On s’intéresse à ce problème pour des algèbres définies sur des sous-ensembles compacts du plan complexe de connectivité finie.
Sur les opérateurs multiplicativement liés dans les algèbres de dimension finie
Sur les transformées de Fourier radiales
Swiss cheeses, rational approximation and universal plane curves
We consider the compact plane sets known as Swiss cheese sets, which are a useful source of examples in the theory of uniform algebras and rational approximation. We develop a theory of allocation maps connected to such sets and we use this theory to modify examples previously constructed in the literature to obtain examples homeomorphic to the Sierpiński carpet. Our techniques also allow us to avoid certain technical difficulties in the literature.
Synthèse et algèbre de multiplicateurs de
Soit , l’espace de Banach des fonctions continues sur qui sont parties réelles de fonctions de l’algèbre du disque . On étudie les ensembles de de synthèse pour et l’algèbre des multiplicateurs de . On en déduit des théorèmes d’approximation dans par des produits de Blaschke.
Tensor product of URM algbras
The Banach algebra of continuous bounded functions with separable support
We prove a commutative Gelfand-Naimark type theorem, by showing that the set of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space X (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to C₀(Y) for some unique (up to homeomorphism) locally compact Hausdorff space Y. The space Y, which we explicitly construct as a subspace of the Stone-Čech compactification of X, is countably compact, and if X is non-separable,...
The characteristic algebra of a polynomial covering map.
The Complex Stone-Weierstrass Property
The compact Hausdorff space X has the CSWP iff every subalgebra of C(X,ℂ) which separates points and contains the constant functions is dense in C(X,ℂ). Results of W. Rudin (1956) and Hoffman and Singer (1960) show that all scattered X have the CSWP and many non-scattered X fail the CSWP, but it was left open whether having the CSWP is just equivalent to being scattered. Here, we prove some general facts about the CSWP; in particular we show that if X is a compact ordered space,...
The fixed point property of unital abelian Banach algebras.
The Fourier algebra of SL(2,...)......, n...2, has no multiplier bounded approximate unit.
The Pełczyński property for some uniform algebras
The structure of homomorphisms from Banach algebras of differentiable functions into finite dimensional Banach algebras.
The Uniform Algebra Generated by z and a Smooth Even Function.
The weak Phillips property
Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.
Theorems of Korovkin type for adapted spaces
It is shown that the methods developed in an earlier paper of the author about a Dirichlet problem for the Silov boundary [Annales Inst. Fourier, 11 (1961)] lead in a new and natural way to the most important results about the convergence of positive linear operators on spaces of continuous functions defined on a compact space. Choquet’s notion of an adapted space of continuous functions in connection with results of Mokobodzki-Sibony opens the possibility of extending these results to the case...