Hyperinvariant subspaces for some compact perturbations of multiplication operators

Hubert Klaja (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

In this paper, a sufficient condition for the existence of hyperinvariant subspace of compact perturbations of multiplication operators on some Banach spaces is presented. An interpretation of this result for compact perturbations of normal and diagonal operators on Hilbert space is also discussed. An improvement of a result of [FX12] for compact perturbations of diagonal operators is also obtained.

Mots clés: invariant subspace problem; hyperinvariant subspace problem; compact perturbations of normal operators; compact perturbations of diagonal operators

Domaines: Analyse fonctionnelle [math.FA]

Hubert Klaja. Hyperinvariant subspaces for some compact perturbations of multiplication operators. 2014. ⟨hal-00863368v3⟩