Common hypercyclic vectors for high dimensional families of operators

2015/03/30 by Frédéric Bayart, Bayart, Frédéric
Mathematics · #Holomorphic and Operator Theory #Advanced Banach Space Theory #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1503.08574

Abstract

Let (T_λ)_λ∈Λ be a family of operators acting on a F-space X, where the parameter space Λ is a subset of \mathbb R^d. We give sufficient conditions on the family to yield the existence of a vector x∈ X such that, for any λ∈Λ, the set \T_λⁿ x; n≥ 1\ is dense in X. We obtain results valid for any value of d≥ 1 whereas the previously known results where restricted to d=1. Our methods also shed new light on the one-dimensional case.

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