Hypercyclic algebras for weighted shifts on trees

2024/11/21 by Abbar, Arafat, Costa, Fernando
#05C05 #46A45 #47A16 #47B37 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2411.14609

Abstract

We study the existence of algebras of hypercyclic vectors for weighted backward shifts on sequence spaces of directed trees with the coordinatewise product. When V is a rooted directed tree, we show the set of hypercyclic vectors of any backward weighted shift operator on the space c₀(V) or ℓ¹(V) is algebrable whenever it is not empty. We provide necessary and sufficient conditions for the existence of these structures on ℓ^p(V), 1

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• Common hypercyclic algebras for families of products of backward shifts
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