Journal of Mathematics and Statistics

Hypercyclic Functions for Backward and Bilateral Shift Operators

N. Faried, Z. A. Hassanain and A. Morsy

DOI : 10.3844/jmssp.2009.178.182

Journal of Mathematics and Statistics

Volume 5, Issue 3

Pages 178-182

Abstract

Problem statement: Giving conditions for bilateral forward and unilateral backward shift operators over the weighted space of p-summable formal series to be hypercyclic. This provides a generalization to the case of Hilbert space. Approach: We used hypercyclicity criterion and some preliminary concepts for formal Laurent series and formal power series. Moreover we got benefits of some duality properties of above mentioned spaces. Results: We obtained necessary and sufficient conditions for bilateral forward and unilateral backward shift operators to be hypercyclic. Conclusion: The bilateral forward shift operator was hypercyclic on the space of all formal Laurent series and the unilateral backward shift operator was hypercyclic on the space of all formal power series under certain conditions.

Copyright

© 2009 N. Faried, Z. A. Hassanain and A. Morsy. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.