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.

Abstract We study the cyclic, supercyclic and hypercyclic properties of a composition operator C ϕ on Segal-Bargmann space ℋ(ℰ), where ( z ) = Az + b , A is bounded linear ℰ, ∈ ℰ with || ⩽ 1 * belongs to range I – )½. Specifically, under some conditions symbol we show that if cyclic then A* but converse need not be true. also cyclic. Further there no ℋ(ℰ) for certain class symbols .