Closed ideals in certain Beurling algebras, and synthesis of hyperdistributions
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