Common hypercyclic algebras for families of products of backward shifts

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