Common hypercyclic algebras for families of products of backward shifts

2021/06/16 by Costa, Fernando
#Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2106.08949

Abstract

In this paper, we generalize to the context of algebras some recent results on the existence of common hypercyclic vectors for families of products of backward shift operators. We also give, in a multi-dimensional setting, a positive answer to a question raised by F. Bayart, D. Papathanasiou and the author about the existence of a common hypercyclic algebra on ℓ₁(ℕ) with the convolution product for the family of backward shifts (B_w(λ))_λ>0 induced by the weights w_n(λ)=1+λ/n.

Related

• Hypercyclic algebras
• Common hypercyclic vectors for families of backward shift operators
• Algebrability of the set of hypercyclic vectors for backward shift\n operators
• Baire theorem and hypercyclic algebras
• Algebras of frequently hypercyclic vectors