The center of topologically primitive galbed algebras
It is shown that every unital σ-complete topologically primitive strongly galbed Hausdorff algebra in which all elements are bounded is central
The structure of a subclass of amenable Banach algebras.
The tensor algebra of power series spaces
The linear isomorphism type of the tensor algebra T(E) of Fréchet spaces and, in particular, of power series spaces is studied. While for nuclear power series spaces of infinite type it is always s, the situation for finite type power series spaces is more complicated. The linear isomorphism T(s) ≅ s can be used to define a multiplication on s which makes it a Fréchet m-algebra . This may be used to give an algebra analogue to the structure theory of s, that is, characterize Fréchet m-algebras...
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 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 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.
Totally convex algebras
By definition a totally convex algebra is a totally convex space equipped with an associative multiplication, i.eȧ morphism of totally convex spaces. In this paper we introduce, for such algebras, the notions of ideal, tensor product, unitization, inverses, weak inverses, quasi-inverses, weak quasi-inverses and the spectrum of an element and investigate them in detail. This leads to a considerable generalization of the corresponding notions and results in the theory of Banach spaces.
Two-sided Banach algebras