Théorème de Cohen-Hewitt dans une algèbre de Jordan-Fréchet.
Théorème de Gelfand-Mazur dans les algèbres p-normées non-associatives.
Théorèmes de factorisation dans les algèbres completes de Jordan.
A generalization of a result of Cohen-Hewitt is given in the case of Jordan-Banach algebras. Some precisions of factorization are obtained.
Théorèmes de factorisation dans les algèbres normées complètes non associatives
Théorèmes de structure sur certaines algèbres m-convexes commutatives.
Nous donnons dans ce travail une caractérisation des algèbres (semi-simples) localement-convexes complètes faiblement topologisées au sens de S. Warner, ce qui clarifie, entre autres, plusiers résultats données sur certaines classes d'algèbres à base étudiées par de nombreux auteurs ([2], [6], [7]) pour approcher le problème de E. A. Michael sur la continuité des caractères dans les algèbres de Fréchet [9].
Théorèmes de structures de certaines algèbres, et continuité des caractères
Topological algebras in which all maximal two-sided ideals are closed
We characterize unital topological algebras in which all maximal two-sided ideals are closed.
Topological algebras of continuous functions over valued fields
Topological Algebras of Functions of Bounded Variation II.
Topological algebras of kernels.
Topological algebras of random elements
Let L₀(Ω;A) be the Fréchet space of Bochner-measurable random variables with values in a unital complex Banach algebra A. We study L₀(Ω;A) as a topological algebra, investigating the notion of spectrum in L₀(Ω;A), the Jacobson radical, ideals, hulls and kernels. Several results on automatic continuity of homomorphisms are developed, including versions of well-known theorems of C. Rickart and B. E. Johnson.
Topological algebras with maximal regular ideals closed
It is shown that all maximal regular ideals in a Hausdorff topological algebra A are closed if the von Neumann bornology of A has a pseudo-basis which consists of idempotent and completant absolutely pseudoconvex sets. Moreover, all ideals in a unital commutative sequentially Mackey complete Hausdorff topological algebra A with jointly continuous multiplication and bounded elements are closed if the von Neumann bornology of A is idempotently pseudoconvex.
Topological algebras with pseudoconvexly bounded elements
It is shown that every commutative sequentially bornologically complete Hausdorff algebra A with bounded elements is representable in the form of an (algebraic) inductive limit of an inductive system of locally bounded Fréchet algebras with continuous monomorphisms if the von Neumann bornology of A is pseudoconvex. Several classes of topological algebras A for which or for each a ∈ A are described.
Topological localization in Fréchet algebras.
Topological modules over strictly minimal topological rings
We study the validity of two basic results of the classical theory of topological vector spaces in the context of topological modules.
Topological radicals, I. Basic properties, tensor products and joint quasinilpotence
Topologically Invertible Elements and Topological Spectrum
Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion is continuous in every invertive Fréchet algebra, and singly generated unital semitopological algebras have continuous characters if and only if the topological spectrum of the generator is non-empty. Several open problems are presented.
Topologie et traces sur les -algèbres
Topologies of compact families on the ideal space of a Banach algebra
Let be a family of compact sets in a Banach algebra A such that is stable with respect to finite unions and contains all finite sets. Then the sets , K ∈ define a topology τ() on the space Id(A) of closed two-sided ideals of A. is called normal if in (Id(A),τ()) and x ∈ A╲I imply . (1) If the family of finite subsets of A is normal then Id(A) is locally compact in the hull kernel topology and if moreover A is separable then Id(A) is second countable. (2) If the family of countable compact sets...
Topologies on the space of ideals of a Banach algebra
Some topologies on the space Id(A) of two-sided and closed ideals of a Banach algebra are introduced and investigated. One of the topologies, namely , coincides with the so-called strong topology if A is a C*-algebra. We prove that for a separable Banach algebra coincides with a weaker topology when restricted to the space Min-Primal(A) of minimal closed primal ideals and that Min-Primal(A) is a Polish space if is Hausdorff; this generalizes results from [1] and [5]. All subspaces of Id(A)...