Toeplitz operators for hypodirichlet algebras
Topological Algebras of Functions of Bounded Variation I.
Topological Algebras of Functions of Bounded Variation II.
Topologies on the Extreme Points of Compact Convex Sets II.
Translation-invariant function algebras on compact abelian groups.
Trivial Jensen measures without regularity
In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point.
Un problème d'extension linéaire dans les algèbres uniformes
Soit une algèbre uniforme et soit un idéal fermé de tel que soit une algèbre isométriquement isomorphe à , il existe alors une sous-algèbre fermée telle que est isométriquement isomorphe à .
Un teorema tipo «Michael» para subálgebras de funciones continuas sobre un espacio de Banach.
Una nota sobre las álgebras de Banach regulares no-arquimedianas.
Es bien conocido que el conjunto M de los ideales maximales de un álgebra de Banach compleja X es un espacio compacto y Hausdorff para la topología de Gelfand, y que X es isométricamente isomorfa al álgebra C(M,C) de las funciones continuas sobre M si y sólo si X es una B*-álgebra, es decir un álgebra de Banach con involución verificando ||x*x|| = ||x||2 (Gelfand-Naimark). En el caso no-arquimediano, X admite tal representación si y sólo si el subespacio vectorial engendrado por {e ∈ X | e2 = e,...
Une note sur la noethérianité
Uniform algebras and analytic multifunctions
Dati due elementi e in un'algebra uniforme , sia . Nella presente Nota si danno, fra l’altro, due nuove dimostrazioni elementari del fatto che la funzione è subarmonica su e che l’applicazione è analitica nel senso di Oka.
Uniform algebras satisfying certain extension properties
Uniform Approximation on Manifolds.
Uniformly continuous functionals on Banach algebras
Uniqueness of complete norms for quotients of Banach function algebras
We prove that every quotient algebra of a unital Banach function algebra A has a unique complete norm if A is a Ditkin algebra. The theorem applies, for example, to the algebra A (Γ) of Fourier transforms of the group algebra of a locally compact abelian group (with identity adjoined if Γ is not compact). In such algebras non-semisimple quotients arise from closed subsets E of Γ which are sets of non-synthesis. Examples are given to show that the condition of Ditkin cannot be relaxed. We construct...
Variations on a theme of Beurling.
Weak amenability and semidirect products in simple Lie groups.
Weak multiplicative operators on function algebras without units
For a function algebra A let ∂A be the Shilov boundary, δA the Choquet boundary, p(A) the set of p-points, and |A| = |f|: f ∈ A. Let X and Y be locally compact Hausdorff spaces and A ⊂ C(X) and B ⊂ C(Y) be dense subalgebras of function algebras without units, such that X = ∂A, Y = ∂B and p(A) = δA, p(B) = δB. We show that if Φ: |A| → |B| is an increasing bijection which is sup-norm-multiplicative, i.e. ||Φ(|f|)Φ(|g|)|| = ||fg||, f,g ∈ A, then there is a homeomorphism ψ: p(B) → p(A) with respect...
Weak spectral synthesis in Fourier algebras of coset spaces
Let G be a locally compact group, K a compact subgroup of G and A(G/K) the Fourier algebra of the coset space G/K. Applying results from [E. Kaniuth, Weak spectral synthesis in commutative Banach algebras, J. Funct. Anal. 254 (2008), 987-1002], we establish injection and localization theorems relating weak spectral sets and weak Ditkin sets for A(G/K) to such sets for A(H/H ∩ K), where H is a closed subgroup of G. We also prove some results towards the analogue of Malliavin's theorem for weak spectral...
Weakly amenable groups and the RNP for some Banach algebras related to the Fourier algebra
It is shown that if G is a weakly amenable unimodular group then the Banach algebra , where is the Figà-Talamanca-Herz Banach algebra of G, is a dual Banach space with the Radon-Nikodym property if 1 ≤ r ≤ max(p,p’). This does not hold if p = 2 and r > 2.