Algebras of frequently hypercyclic vectors

Abstract

We show that the multiples of the backward shift operator on the spaces , 1 ≤ < ∞, or 0 , when endowed with coordinatewise multiplication, do not possess frequently hypercyclic algebras. More generally, we characterize the existence of algebras of -hypercyclic vectors for these operators. We also show that the differentiation operator on the space of entire functions, when endowed with the Hadamard product, does not possess frequently hypercyclic algebras. On the other hand, we show that for any frequently hypercyclic operator on any Banach space, ( ) is algebrable for a suitable product, and in some cases it is even strongly algebrable. K E Y W O R D S-hypercyclic vector, algebrability, Banach algebra, frequently hypercyclic vector, weighted shift 1120

Linear Dynamical Systems

“…Let Φ be a nonconstant polynomial with Φ(0) = 0. Then the The topic of hypercyclic algebras is rapidly evolving and research is expanding into different directions such as the investigation of frequently hypercyclic algebras [71], [14].…”

Linear Dynamical Systems

“…The topic of hypercyclic algebras is rapidly evolving and research is expanding into different directions such as the investigation of frequently hypercyclic algebras [70], [14].…”