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Complex Analysis and Operator Theory

, Volume 13, Issue 1, pp 257–274 | Cite as

Dynamics of Generalised Derivations and Elementary Operators

  • Clifford GilmoreEmail author
Article

Abstract

We identify concrete examples of hypercyclic generalised derivations acting on separable ideals of operators and establish some necessary conditions for their hypercyclicity. We also consider the dynamics of elementary operators acting on particular Banach algebras, which reveals surprising hypercyclic behaviour on the space of bounded linear operators on the Banach space constructed by Argyros and Haydon.

Keywords

Hypercyclic Generalised derivation Elementary operator 

Mathematics Subject Classification

Primary 47A16 Secondary 47B47 

Notes

Acknowledgements

This article is part of the Ph.D. thesis of the author and he would like to thank his supervisor Hans-Olav Tylli for helpful comments and remarks during its preparation.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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