Spectral characterization of weak topological transitivity

Original Paper

Abstract

Given a bounded linear operator S on a real Banach space X, we characterize weak topological transitivity of the operator families \({\lbrace S^t \mid t \in {\mathbb N}\rbrace}\), \({\lbrace \kappa S^t\mid\, t \in {\mathbb N},\, \kappa >0 \rbrace}\), and \({\lbrace \kappa S^t\mid\, t \in {\mathbb N},\, \kappa \in {\mathbb R}\rbrace}\) in terms of the point spectrum of the dual operator S*.

Keywords

Hypercyclic semigroups Weak topology Topological transitivity 

Mathematics Subject Classification (2000)

47A16 47D03 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institute of Mathematics and Scientific ComputingKarl-Franzens-Universität GrazGrazAustria

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