Some characterizations of complex normed Q-algebras.
Some module cohomological properties of Banach algebras
We find some relations between module biprojectivity and module biflatness of Banach algebras and and their projective tensor product . For some semigroups , we study module biprojectivity and module biflatness of semigroup algebras .
Stability of commuting maps and Lie maps
Let A be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on A is near an actual commuting continuous linear (resp. quadratic) map on A. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.
Strongly compact algebras.
An algebra of bounded linear operators on a Hilbert space is said to be strongly compact if its unit ball is relatively compact in the strong operator topology. A bounded linear operator on a Hilbert space is said to be strongly compact if the algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. First of all, some basic properties of strongly compact algebras...
Structure -convexe d’une algèbre limite inductive localement convexe d’algèbres de Banach
Structure of locally idempotent algebras.
Structure theory of homologically trivial and annihilator locally C*-algebras
We study the structure of certain classes of homologically trivial locally C*-algebras. These include algebras with projective irreducible Hermitian A-modules, biprojective algebras, and superbiprojective algebras. We prove that, if A is a locally C*-algebra, then all irreducible Hermitian A-modules are projective if and only if A is a direct topological sum of elementary C*-algebras. This is also equivalent to A being an annihilator (dual, complemented, left quasi-complemented, or topologically...
Superstability for generalized module left derivations and generalized module derivations on a Banach module. I.
Sur la transformation de Dirac d'un espace à génération compacte
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
Über die Ecken des numerischen Wertebereches in einer Banachalgebra.