Title :

A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces

Author(s) :

Grivaux, Sophie [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Roginskaya, Maria [Auteur]
Department of Mathematical Sciences [Chalmers]

Journal title :

Proceedings of the London Mathematical Society

Pages :

596 - 652

Publisher :

London Mathematical Society

Publication date :

2014

ISSN :

0024-6115

English keyword(s) :

Invariant Subspace and Invariant Subset Problems on Banach spaces
cyclic and hypercyclic vectors
orbits of linear operators
Read’s type operators
quasi-reflexive spaces
weakly compact operators

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

We present a general method for constructing operators without non-trivial invariant closed subsets on a large class of non-reflexive Banach spaces. In particular, our approach unifies and generalizes several constructions ...
Show more >We present a general method for constructing operators without non-trivial invariant closed subsets on a large class of non-reflexive Banach spaces. In particular, our approach unifies and generalizes several constructions due to Read of operators without nontrivial invariant subspaces on the spaces l_1, c_0 or ⊕_2 J, and without non-trivial invariant subsets on l_1. We also investigate how far our methods can be extended to the Hilbertian setting, and construct an operator on a quasireflexive dual Banach space which has no nontrivial w *-closed invariant subspace.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T15:34:56Z