Common hypercyclic algebras for families of products of backward shifts (Q2247737)

This article generalizes to the context of algebras some recent results on the existence of common hypercyclic vectors for families of products of backward shift operators. Conditions are give to ensure the existence of a common hypercyclic algebra. Two classical products are commonly considered on sequence algebras: the coordinatewise product and the convolution (or Cauchy) product. A~positive answer, in a multi-dimensional setting, to a question raised by \textit{F. Bayart, D. Papathanasiou} and the author [``Common and disjoint hypercyclic algebras'', Isr. J. Math. (to appear), \url{doi:10.1007/s11856-022-2337-z}] about the existence of a common hypercyclic algebra on \(\ell_1(\mathbb{N})\) with the convolution product for the family of backward shifts induced by the weights \(w_n(\lambda)=1 + \lambda/n\) is also presented.