On regularities and Fredholm theory
We investigate the relationship between the regularities and the Fredholm theory in a Banach algebra.
On Riesz and Inessential Operators.
On the abstract theorem of Picard.
On the Arens products and reflexive Banach algebras.
On the contracted -algebra of a polycyclic monoid.
On the ideals of extended quasi-nilpotent Banach algebras.
On the range of n th order derivations acting on commutative Banach positive squares ℓ-algebras
In this paper we prove that the image of a nth order derivation on real commutative Banach ℓ-algebras with positive squares is contained in the set of nilpotent elements.
On the ranks of Elements of Semiprime Banach Algebras
On topological algebras
Polynomially compact elements of Banach algebras
Primary Ideals in Beurling Algebras.
Prime Ideals in the C*-algebra of a Nilpotent Group.
Primitive Ideals in Tensor Products of Banach Algebras.
Propriétés spectrales en analyse non archimédienne
Range inclusion results for derivations on noncommutative Banach algebras
Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes a result...
Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems
As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.
Reductive Algebras with Minimal Ideals.
Remarks on Segal Algebras.
Renormalizations of Banach and locally convex algebras
Representations of bornological algebras.