Title :

Typicality of operators on Fréchet algebras admitting a hypercyclic algebra

Author(s) :

Alexandre, William [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Gilmore, Clifford [Auteur]
Laboratoire de Mathématiques Blaise Pascal [LMBP]
Grivaux, Sophie [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Hypercyclic operators
hypercyclic algebras
Fréchet spaces of holomorphic functions
differentiation operator
eigenvector fields

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fr\'echet algebras, endowed with the topology of pointwise convergence. Our ...
Show more >This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fr\'echet algebras, endowed with the topology of pointwise convergence. Our main results show that within natural Polish spaces of continuous operators acting on the algebra $H(\mathbb{C})$ of entire functions on $\mathbb{C}$, a typical operator supports a hypercyclic algebra. We also investigate the case of the complex Fr\'echet algebras $X=\ell_{p}(\mathbb{N})$, $1\le p<+\infty$, or $X=c_{0}(\mathbb{N})$ endowed with the coordinatewise product, and show that whenever $M>1$, a typical operator on $X$ of norm less than or equal to $M$ admits a hypercyclic algebra.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL