On 1-parameter subgroups of the circle-exponent function in A-convex topological algebras.
On a certain class of subspectra
The aim of this paper is to characterize a class of subspectra for which the geometric spectral radius is the same and depends only upon a commuting -tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity.
On a class of inner maps
Let be a continuous map of the closure of the open unit disc of into a unital associative Banach algebra , whose restriction to is holomorphic, and which satisfies the condition whereby for all and whenever (where is the spectrum of any ). One of the basic results of the present paper is that is , that is to say, is then a compact subset of that does not depend on for all . This fact will be applied to holomorphic self-maps of the open unit ball of some -algebra...
On a class of topological algebras. (Sur une classe d'algèbres topologiques.)
On a problem of Bertram Yood
In 1964, Bertram Yood posed the following problem: whether the intersection of all closed maximal regular left ideals of a topological ring coincides with the intersection of all closed maximal regular right ideals of this ring. It is proved that these two intersections coincide for advertive and simplicial topological rings and, using this result, it is shown that the topological left radical and the topological right radical for every advertive and simplicial topological algebra coincide.
On a question of A. Wilansky in normed algebras
On A-convex and lm-convex algebra structures of a locally convex space
Given a locally convex space (V,Γ), we find (all) the multiplications π on V (associative or not) such that the algebra A ≡ (V,π,Γ) becomes (i) A-convex, (ii) lm-convex.
On ...-admissible Vector Space Topologies on C(X).
On Banach algebras satisfying a spectral maximum principle
On Cental Morphisms
On certain products of Banach algebras with applications to harmonic analysis
Given Banach algebras A and B with spectrum σ(B) ≠ ∅, and given θ ∈ σ(B), we define a product , which is a strongly splitting Banach algebra extension of B by A. We obtain characterizations of bounded approximate identities, spectrum, topological center, minimal idempotents, and study the ideal structure of these products. By assuming B to be a Banach algebra in ₀(X) whose spectrum can be identified with X, we apply our results to harmonic analysis, and study the question of spectral synthesis,...
On certain quasi-complemented and complemented Banach algebras.
On circle-Exponential Topological Algebras
On Continuity of Algebra Homomorphisms and Uniqueness of Metric Topology.
On discontinuity of the spectral radius in Banach algebras
On domination problem in Banach algebras
On Gelfand-Mazur theorem on a class of F -algebras
A topological algebra A is said to be fundamental if there exists b > 1 such that for every sequence (xn) in A, (xn) is Cauchy whenever the sequence bn(xn − xn-1) tends to zero as n → ∞. Let A be a complex unital fundamental F-algebra with bounded elements such that A* separates the points on A. Then we prove that the spectrum σ(a) of every element a ∈ A is nonempty compact. Moreover, if A is a division algebra, then A is isomorphic to the complex numbers ℂ. This result is a generalization of...
On generalized right modular complemented algebras
On generalized topological divisors of zero
On inductive limits of topological algebras