Hostname: page-component-cb9f654ff-h4f6x Total loading time: 0 Render date: 2025-08-25T21:59:50.071Z Has data issue: false hasContentIssue false
  • English
  • Français

Hypercyclicity of Semigroups is a Very Unstable Property

Published online by Cambridge University Press:  23 October 2008

W. Desch  and
W. Schappacher
W. Desch
Affiliation:
Karl-Franzens-Universität Graz, Institut für Mathematik und wissenschaftliches Rechnen Heinrichstraße 36, A-8010 Graz, Austria
W. Schappacher*
Affiliation:
Karl-Franzens-Universität Graz, Institut für Mathematik und wissenschaftliches Rechnen Heinrichstraße 36, A-8010 Graz, Austria
*
georg.desch@uni-graz.at
Get access

Abstract

Hypercyclicity of C0-semigroups is a very unstable property: We give examples toshow that adding arbitrary small constants or a bounded rank one operator to the generator of ahypercyclic semigroup can destroy hypercyclicity. Also the limit of hypercyclic semigroups (evenin operator norm topology) need not be hypercyclic, and a hypercyclic semigroup can be the limitof nonhypercyclic ones. Hypercyclicity is not inherited by the Yosida approximations. Finally, therestriction of a hypercyclic nonnegative semigroup in a Banach lattice to the positive cone may befar from hypercyclic.

Keywords

hypercyclic semigroupsperturbation

Information

Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 3 , Issue 7: Special issue dedicated to Glenn Webb , 2008 , pp. 148 - 160
Copyright
© EDP Sciences, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable