Hypercyclic Functions for Backward and Bilateral Shift Operators

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.