Bounded derivations on commutative semigroups.
Bounded projections, duality, and multipliers in spaces of harmonic functions.
Bounded structures of uniformly A-convex algebras.
Bourgain algebras of G-disc algebras
Bundles of Banach algebras.
Calcul fonctionnel holomorphe dans les algèbres de Banach ultramétriques
Calcul symbolique sur la frontière de Silov de certaines algèbres de fonctions holomorphes
On démontre un résultat de dichotomie pour les fonctions qui opèrent sur les restrictions d’algèbres de fonctions holomorphes de plusieurs variables. On obtient ce résultat après étude de la séparation par des fonctions holomorphes de compacts sur certaines hypersurfaces de .
Caractérisation des anneaux noethériens de séries formelles à croissance controlée. Application à la synthèse spectrale.
Given a subring of the ring of formal power series defined by the growth of the coefficients, we prove a necessary and sufficient condition for it to be a noetherian ring. As a particular case, we show that the ring of Gevrey power series is a noetherian ring. Then, we get a spectral synthesis theorem for some classes of ultradifferentiable functions.
Category theorems for certain Banach spaces of analytic functions.
Central decompositions for compact convex sets
Characterizations of amenable representations of compact groups
Let G be a locally compact group and let π be a unitary representation. We study amenability and H-amenability of π in terms of the weak closure of (π ⊗ π)(G) and factorization properties of associated coefficient subspaces (or subalgebras) in B(G). By applying these results, we obtain some new characterizations of amenable groups.
Characterizing algebras of -functions on manifolds
Among all -algebras we characterize those which are algebras of -functions on second countable Hausdorff -manifolds.
Charakterisierungen einiger Funktionenalgebren.
Closed ideals of A+ and the Cantor set.
Closed ideals with countable hull in algebras of analytic functions smooth up to the boundary.
Cohomology theory on non commutative algebras of continuous functions
Common zero sets of equivalent singular inner functions
Let μ and λ be bounded positive singular measures on the unit circle such that μ ⊥ λ. It is proved that there exist positive measures μ₀ and λ₀ such that μ₀ ∼ μ, λ₀ ∼ λ, and , where is the associated singular inner function of μ. Let be the common zeros of equivalent singular inner functions of . Then (μ) ≠ ∅ and (μ) ∩ (λ) = ∅. It follows that μ ≪ λ if and only if (μ) ⊂ (λ). Hence (μ) is the set in the maximal ideal space of which relates naturally to the set of measures equivalent to μ....
Common zero sets of equivalent singular inner functions II
We study connected components of a common zero set of equivalent singular inner functions in the maximal ideal space of the Banach algebra of bounded analytic functions on the open unit disk. To study topological properties of zero sets of inner functions, we give a new type of factorization theorem for inner functions.
Commutative Banach Algebras and Decomposable Operators.
Commutative, radical amenable Banach algebras
There has been a considerable search for radical, amenable Banach algebras. Noncommutative examples were finally found by Volker Runde [R]; here we present the first commutative examples. Centrally placed within the construction, the reader may be pleased to notice a reprise of the undergraduate argument that shows that a normed space with totally bounded unit ball is finite-dimensional; we use the same idea (approximate the norm 1 vector x within distance η by a “good” vector ; then approximate...