Topological and algebraic genericity of divergence and universality
Volume 167 / 2005
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.
