Topological and algebraic genericity of divergence and universality

Volume 167 / 2005

Frédéric Bayart Studia Mathematica 167 (2005), 161-181 MSC: Primary 46B25, 47A16. DOI: 10.4064/sm167-2-4

Abstract

We give general theorems which assert that divergence and universality of certain limiting processes are generic properties. We also define the notion of algebraic genericity, and prove that these properties are algebraically generic as well. We show that universality can occur with Dirichlet series. Finally, we give a criterion for the set of common hypercyclic vectors of a family of operators to be algebraically generic.

Authors

  • Frédéric BayartLaboratoire Bordelais d'Analyse et de Géométrie
    UMR 5467
    Université Bordeaux 1
    351 Cours de la Libération
    F-33405 Talence Cedex, France
    e-mail

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