The characteristic algebra of a polynomial covering map.
The compactum of a semi-simple commutative Banach algebra.
The group of invertible elements of a commutative Banach algebra
The kh-socle of a commutative semisimple Banach algebra
Let be a commutative complex semisimple Banach algebra. Denote by the kernel of the hull of the socle of . In this work we give some new characterizations of this ideal in terms of minimal idempotents in . This allows us to show that a “result” from Riesz theory in commutative Banach algebras is not true.
The norm spectrum in certain classes of commutative Banach algebras
Let A be a commutative Banach algebra and let be its structure space. The norm spectrum σ(f) of the functional f ∈ A* is defined by , where f·a is the functional on A defined by ⟨f·a,b⟩ = ⟨f,ab⟩, b ∈ A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.
The strong spectral extension property does not imply the multiplicative Hahn-Banach property
An example is given of a semisimple commutative Banach algebra that has the strong spectral extension property but fails the multiplicative Hahn-Banach property. This answers a question posed by M. J. Meyer in [4].
The structure of a class of Banach algebras generated by a Banach space
The trace of finite and nuclear elements in Banach algebras
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].
Topología grassmaniana sobre los ideales cerrados de codimensión finita de un álgebra de Banach conmutativa.
Topological algebras with an orthogonal total sequence
The aim of this paper is an investigation of topological algebras with an orthogonal sequence which is total. Closed prime ideals or closed maximal ideals are kernels of multiplicative functionals and the continuous multiplicative functionals are given by the “coefficient functionals”. Our main result states that an orthogonal total sequence in a unital Fréchet algebra is already a Schauder basis. Further we consider algebras with a total sequence satisfying and for all n ∈ ℕ.
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.
Topologies et compactologies