Questions in linear recurrence: From the T ⊕ T -problem to lineability

Grivaux, Sophie; López-Martínez, Antoni; Peris, Alfred

Type de document :

Pré-publication ou Document de travail

Titre :

Questions in linear recurrence: From the T ⊕ T -problem to lineability

Auteur(s) :

Grivaux, Sophie [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
López-Martínez, Antoni [Auteur]
Peris, Alfred [Auteur]

Mot(s)-clé(s) en anglais :

Linear dynamical systems
hypercyclicity
recurrence
quasi-rigidity
lineability.

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

We study, for a continuous linear operator T on an F-space X, when the direct sum operator T ⊕ T is recurrent on X ⊕ X. In particular: we establish the analogous notion, for recurrence, to that of (topological) weak-mixing ...
Lire la suite >We study, for a continuous linear operator T on an F-space X, when the direct sum operator T ⊕ T is recurrent on X ⊕ X. In particular: we establish the analogous notion, for recurrence, to that of (topological) weak-mixing for transitivity/hypercyclicity, namely quasi-rigidity; and we construct a recurrent but not quasi-rigid operator on each separable infinite-dimensional Banach space, solving the T ⊕ T-recurrence problem in the negative way. The quasi-rigidity notion is closely related to the dense lineability of the set of recurrent vectors, and using similar conditions we study the lineability and dense lineability properties for the set of F-recurrent vectors, under very weak assumptions on the Furstenberg family F.Lire moins >

Langue :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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