Les -algèbres à idéaux premiers totalement ordonnés par inclusion sont de Fréchet
Les semi-normes sur les algèbres d'éléments analytiques au sens de Krasner
Linear maps preserving the generalized spectrum.
Let H be an infinite-dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. For an operator T in B(H), let σg(T) denote the generalized spectrum of T. In this paper, we prove that if φ: B(H) → B(H) is a surjective linear map, then φ preserves the generalized spectrum (i.e. σg(φ(T)) = σg(T) for every T ∈ B(H)) if and only if there is A ∈ B(H) invertible such that either φ(T) = ATA-1 for every T ∈ B(H), or φ(T) = ATtrA-1 for every T ∈ B(H). Also, we...
Local Banach algebras as Henselian rings
Locally compact Baer rings.
Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras
Let be a locally A-pseudoconvex algebra over or . We define a new topology on which is the weakest among all m-pseudoconvex topologies on stronger than . We describe a family of non-homogeneous seminorms on which defines the topology .
Lusin sets and generalized spectra of topological algebras
Minimal incomplete norms on Banach algebras
We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.
Module maps over locally compact quantum groups
We study locally compact quantum groups and their module maps through a general Banach algebra approach. As applications, we obtain various characterizations of compactness and discreteness, which in particular generalize a result by Lau (1978) and recover another one by Runde (2008). Properties of module maps on are used to characterize strong Arens irregularity of L₁() and are linked to commutation relations over with several double commutant theorems established. We prove the quantum group...
Motzkin factorization in algebras of analytic elements
Multiplicative functionals and entire functions
Let A be a complex Banach algebra with a unit e, let T, φ be continuous functionals, where T is linear, and let F be a nonlinear entire function. If T ∘ F = F ∘ φ and T(e) = 1 then T is multiplicative.
Multiplicative functionals and entire functions, II
Let A be a complex Banach algebra with a unit e, let F be a nonconstant entire function, and let T be a linear functional with T(e)=1 and such that T∘F: A → ℂ is nonsurjective. Then T is multiplicative.
Multipliers of topological algebras [Book]
Multipliers on Banach algebras
Multipliers, self-induced and dual Banach algebras [Book]
Nil, nilpotent and PI-algebras
The notions of nil, nilpotent or PI-rings (= rings satisfying a polynomial identity) play an important role in ring theory (see e.g. [8], [11], [20]). Banach algebras with these properties have been studied considerably less and the existing results are scattered in the literature. The only exception is the work of Krupnik [13], where the Gelfand theory of Banach PI-algebras is presented. However, even this work has not get so much attention as it deserves. The present paper...
Noetherian Banach Algebras are Finite Dimensional.
Noninvertibility preservers on Banach algebras
It is proved that a linear surjection , which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective.
Normal subgroups of classical groups over Banach algebras.
Normally subregular systems in normed algebras