Closed ideals in locally convex algebras of analytic functions.
Closed Ideals in Subalgebras of Banach Algebras II: Ditkin's Condition.
Commutators in Banach *-algebras
The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.
Commutators of quasinilpotents and invariant subspaces
It is proved that the set Q of quasinilpotent elements in a Banach algebra is an ideal, i.e. equal to the Jacobson radical, if (and only if) the condition [Q,Q] ⊆ Q (or a similar condition concerning anticommutators) holds. In fact, if the inner derivation defined by a quasinilpotent element p maps Q into itself then p ∈ Rad A. Higher commutator conditions of quasinilpotents are also studied. It is shown that if a Banach algebra satisfies such a condition, then every quasinilpotent element has some...
Compactness conditions for elementary operators
Various topics concerning compact elementary operators on Banach algebras are studied: their ranges, their coefficients, and the structure of algebras having nontrivial compact elementary operators. In the first part of the paper we consider separately elementary operators of certain simple types. In the second part we obtain our main results which deal with general elementary operators.
Comparisons between different spectra of an element in a Banach algebra.
Complemented *-primitive Ideals in L1-algebras of Exponential Lie Groups and of Motion Groups.
Continuity of a homomorphism on commutative subalgebras is not sufficient for continuity
Counterexample on semiradial Banach algebras
Der Primidealraum der C*-Algebra und die unzerlegebaren Charaktere der Gruppe GI (...,q).
Ditkin's Theorem and ...SIN...-Groups.
Dual complementors in topological algebras
We deal with dual complementors on complemented topological (non-normed) algebras and give some characterizations of a dual pair of complementors for some classes of complemented topological algebras. The study of dual complementors shows their deep connection with dual algebras. In particular, we refer to Hausdorff annihilator locally C*-algebras and to proper Hausdorff orthocomplemented locally convex H*-algebras. These algebras admit, by their nature, the same type of dual pair of complementors....
Elementary operators and subhomogeneous -algebras. II.
Etude d'ensembles de Ditkin fort dans les algèbres tensorielles et les algèbres de groupe.
Extensions of topological algebras.
Extreme spectral states and multiplicative extensions in Banach algebras
Finite generation in C*-algebras and Hilbert C*-modules
We characterize C*-algebras and C*-modules such that every maximal right ideal (resp. right submodule) is algebraically finitely generated. In particular, C*-algebras satisfy the Dales-Żelazko conjecture.
Finite spectra and quasinilpotent equivalence in Banach algebras
This paper further investigates the implications of quasinilpotent equivalence for (pairs of) elements belonging to the socle of a semisimple Banach algebra. Specifically, not only does quasinilpotent equivalence of two socle elements imply spectral equality, but also the trace, determinant and spectral multiplicities of the elements must agree. It is hence shown that quasinilpotent equivalence is established by a weaker formula (than that of the spectral semidistance). More generally, in the second...
Finite-dimensional ideals in Banach algebras
Finiteness properties of topological algebras, I