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FREQUENTLY HYPERCYCLIC BILATERAL SHIFTS

Part of: Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  20 June 2018

KARL-G. GROSSE-ERDMANN Open the ORCID record for KARL-G. GROSSE-ERDMANN [Opens in a new window]
KARL-G. GROSSE-ERDMANN*
Affiliation:
Département de Mathématique, Institut Complexys, Université de Mons, 20 Place du Parc, 7000 Mons, Belgium e-mail: kg.grosse-erdmann@umons.ac.be
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Abstract

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It is not known whether the inverse of a frequently hypercyclic bilateral weighted shift on c0(ℤ) is again frequently hypercyclic. We show that the corresponding problem for upper frequent hypercyclicity has a positive answer. We characterise, more generally, when bilateral weighted shifts on Banach sequence spaces are (upper) frequently hypercyclic.

MSC classification

Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary: 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 2 , May 2019 , pp. 271 - 286
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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