Displaying similar documents to “Invariant subspaces and spectral mapping theorems”

Commutators of quasinilpotents and invariant subspaces

A. Katavolos, C. Stamatopoulos (1998)

Studia Mathematica

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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...

Spectrum for a solvable Lie algebra of operators

Daniel Beltiţă (1999)

Studia Mathematica

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A new concept of spectrum for a solvable Lie algebra of operators is introduced, extending the Taylor spectrum for commuting tuples. This spectrum has the projection property on any Lie subalgebra and, for algebras of compact operators, it may be computed by means of a variant of the classical Ringrose theorem.

Nilpotent elements and solvable actions.

Mihai Sabac (1996)

Collectanea Mathematica

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In what follows we shall describe, in terms of some commutation properties, a method which gives nilpotent elements. Using this method we shall describe the irreducibility for Lie algebras which have Levi-Malçev decomposition property.

The continuity of Lie homomorphisms

Bernard Aupetit, Martin Mathieu (2000)

Studia Mathematica

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We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.