Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

On a hypercylicity criterion for strongly continuous semigroups

Pages: 271 - 275, Volume 13, Issue 2, July 2005      doi:10.3934/dcds.2005.13.271

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Samir EL Mourchid - Département de Mathématiques, Université Cadi Ayyad, Marrakech, B.P.: 2390, Morocco (email)

Abstract: In this note we extend the hypercyclicity criterion (HC) to $C_0$- semigroups on separable Banach spaces and characterize semigroups satisfying (HC). Using (HC) we show the hypercyclicity of the translation group on the weighted spaces $L^p_\rho(\mathbb R,\mathbb C)$ or $C_{0,\rho}(\mathbb R,\mathbb C)$ for admissible weight functions $\rho$.

Keywords:  Hypercyclic semigroups, hypercyclicity criterion, topologically transitive
Mathematics Subject Classification:  47A16, 47D06, 47B37

Received: March 2004;      Revised: January 2005;      Available Online: April 2005.