Dynamics of weighted shifts on ℓp-sums and c0-sums

[en] We investigate a generalization of weighted shifts where each weight wk is replaced by an operator Tk going from a Banach space Xk to another one Xk−1. We then look if the obtained shift operator B(Tk) defined on the ℓp-sum (or the c0-sum) of the spaces Xk is hypercyclic, weakly mixing, mixing, chaotic or frequently hypercyclic. We also compare the dynamical properties of T and of the corresponding shift operator BT. Finally, we interpret some classical criteria in Linear Dynamics in terms of the dynamical properties of a shift operator.

Disciplines :

Mathematics

Author, co-author :

Menet, Quentin ; Université de Mons - UMONS > Faculté des Sciences > Service de Probabilité et statistique

Papathanasiou, Dimitris; Sabanci University, Istanbul, Turkey

Language :

English

Title :

Dynamics of weighted shifts on ℓp-sums and c0-sums

Publication date :

June 2025

Journal title :

Advances in Mathematics

ISSN :

0001-8708

eISSN :

1090-2082

Publisher :

Academic Press Inc.

Volume :

470

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0001870825001483?httpAccept=text/xml

Research unit :

S844 - Probabilité et statistique

Research institute :

R150 - Institut de Recherche sur les Systèmes Complexes

Funders :

FRS-FNRS

Funding text :

The first author is a Research Associate of the Fonds De La Recherche Scientifique - FNRS.

Available on ORBi UMONS :

since 30 May 2025

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